ICMS »

26th British Topology Meeting 2011

Sep 01, 2011 - Sep 03, 2011

ICMS, 15 South College Street Edinburgh

Organisers

Name	Institution
Howie, Jim	Heriot-Watt University
Ranicki, Andrew	University of Edinburgh

The 26th British Topology Meeting will take place in Edinburgh from Thursday 1 to Saturday 3 September 2011. There will be a number of contributed talks as well as invited talks in a broad range of topics in topology.

This event is being supported by the London Mathematical Society, the Edinburgh Mathematical Society and the Glasgow Mathematical Journal Trust.

Invited speakers
Javier Aramayona (Galway)
Stefan Friedl (Cologne)
Jacob Rasmussen (Cambridge)
Saul Schleimer (Warwick)
Catharina Stroppel (Bonn)
Ulrike Tillmann (Oxford)
Karen Vogtmann (Cornell)

Arrangements

Venue
The meeting will take place in the Newhaven lecture theatre at ICMS, 15 South College Street, Edinburgh, EH8 9AA Scotland.

The meeting will begin with registration at 13.30 on Thursday 1 September with the first talk starting at 14.30. The meeting will close early afternoon on Saturday 3 September.

Participants are asked to complete the registration form on this page. There is a £45 registration fee payable for this workshop.

There will be a workshop dinner on Friday 2 September. A fee of £30 will be charged for the dinner

Travel
Information about travel to the UK and Edinburgh is available here. Lothian buses charge 1.30 GBP for a single journey and 3.20 GBP for a day ticket. Please note that the exact fare is required and no change is given.

A taxi directly from the airport will cost approximately 18.00 to 20.00 GBP to the city centre for a one-way journey.

From the airport, you can take the airport bus Airlink to the city centre. It will cost you 3.50 GBP for a single ticket, or 6.00 GBP return. More details on the airport bus Airlink is available here. The bus will take you to Waverley Bridge (next to Waverley Railway Station).

If travelling by train, please note that Edinburgh has two railway stations - Waverley Railway Station being the main station and closest to the workshop venue at ICMS. If you alight at Edinburgh Waverley, the workshop venue is an easy 10 minute walk over North and South Bridge map. The second railway station is called Haymarket and is at the West End of the city centre.

This map shows the location of ICMS.

Please note that it is your responsibility to have adequate travel insurance to cover medical and other emergencies that may occur on your trip.

Programme

Thursday 1 September

13.30 - 14.30	Registration at ICMS
14.30 - 15.30	Jacob Rasmussen (University of Cambridge) Khovanov homology of torus knots
15.30	Coffee/Tea, the Chapterhouse (ground floor)
16.00 - 17.00	Catharina Stroppel (University of Bonn) Categorification and fractional Euler characteristics
17.10	Silvia-Otilia Corduneanu (Gh. Asachi Technical University of Iasi) Topologies on spaces of almost periodic measures
17.20	Anca Croitoru (Al.I. Cuza University of Iasi) Convergence properties for sequences of measurable multifunctions
17.30 - 18.30	Informal wine reception the Chapterhouse (ground floor)

Friday 2 September

10.00 - 11.00	Stefan Friedl (University of Cologne) Fundamental groups of 3-manifolds
11.00 - 11.30	Coffee/Tea, the Chapterhouse (ground floor)
11.30 - 12.30	Karen Vogtmann (Cornell University) Hairy graphs and the cohomology of Out(F_n)
12.30 - 14.00	Lunch in the Chapterhouse (ground floor)
14.00 - 15.00	Javier Aramayona (NUI Galway) Homomorphisms between mapping class groups
15.00 - 15.30	Coffee/Tea, the Chapterhouse (ground floor)
15.30 - 16.30	Saul Schleimer (University of Warwick) The structure theorem for train track splitting sequences
16.40 - 17.40	Ulrike Tillmann (University of Oxford) Homology stability for some families of diffeomorphisms of manifolds
19.00	Dinner at St Trinnean's Room, St Leonards Hall (£30 fee payable)

Saturday 3 September

09.00	Richard Hepworth (University of Copenhagen and University of Aberdeen) Configuration spaces and higher categories
09.20	Mark Grant (University of Edinburgh and University of Nottingham) On immersions in homology classes
09.40	Neset Deniz Turgay (University of Swansea) Conjugation invariants in the dual Leibniz-Hopf algebra
10.00	Spiros Adams-Florou (University of Edinburgh) A controlled Vietoris-like theorem for simplicial complexes
10.20	Pokman Cheung (University of Sheffield) Equivariant chiral differential operators and associated modules
10.40	Thomas Huettemann (Queen's University Belfast) A toric finiteness criterion for chain complexes over Laurent rings
11.00 - 11.30	Coffee/Tea, the Chapterhouse (ground floor)
11.30	Mikael Vejdemo Johansson (St. Andrews) Persistent cohomology and its applications
11.50	Andy Baker (University of Glasgow) Loop spaces with polynomial cohomology
12.10	Michael Wiemeler (University of Manchester) Non-abelian Lie-groups acting on quasitoric manifolds
12.30	Anssi Lahtinen (University of Copenhagen) String topology of classifying spaces
12.50	Andrew Donald (University of Glasgow) Embedding Seifert manifolds in the 4- sphere
13.10	Workshop closes

Presentations:

Presentation Details
Adams-Florou, Spiros
A controlled Vietoris-like theorem for simplicial complexes.
View Abstract Hide Abstract
In 1927 Vietoris proved that if a surjective map of compact metric spaces has acyclic point inverses then the map induces isomorphisms in homology. Modern controlled topology is concerned with various versions of the Vietoris theorem and its converse, using algebraic categories which depend on an input space to characterize maps with small point inverses. Working with chain complexes rather than homology I shall present controlled analogues of Vietoris' Theorem and its converse, for simplicial complexes and homology manifolds. A simplicial map is homotopic to a map with contractible point inverses if and only if it induces a chain equivalence in an appropriate controlled category. A simplicial complex is a homology manifold if and only if it has Poincare duality in an appropriate controlled category.
Aramayona, Javier
Homomorphisms between mapping class groups
View Abstract Hide Abstract
The mapping class group Map(X) of a surface X is the group of self-homeomorphisms of X up to homotopy. In this talk, we will describe all homomorphisms Map(X) to Map(Y), where X and Y are surfaces of finite topological type, with genus(X) > 5 and genus(Y) < 2*genus(X). This is joint work with Juan Souto.
Baker, Andrew
Loop spaces with polynomial cohomology
View Abstract Hide Abstract
In this talk I will identify conditions under which the cohomology $H^*(Omega Mxi;k)$ for the loop space $Omega Mxi$ of the Thom space $Mxi$ of a spherical fibration can be a polynomial ring. We use the Eilenberg-Moore spectral sequence which has a particularly simple form when the Euler class $e(xi)in H^n(B;k)$ vanishes, or equivalently when an orientation class has trivial square. As a consequence of homological calculations we are able to show that the suspension spectrum $Sigma^inftyOmega Mxi$ has a local splitting replacing the James splitting of $SigmaOmega Mxi$ when $Mxi$ is a suspension.
Cheung, Pokman
Equivariant chiral differential operators and associated modules
View Abstract Hide Abstract
The goal of this talk is to outline a construction of what should be the spinor bundle and Dirac operator on the "formal loop space" of a smooth string manifold. This gives a description of the Witten genus that depends on a string structure. Our approach uses the theory of vertex algebras, or more specifically, chiral differential operators (CDOs). Background on CDOs will be provided. Then we will discuss our work, which consists of two steps: (i) lifting a Lie group action on a manifold to a formal loop group action on CDOs, and (ii) using the said action and semi-infinite cohomology to construct vector bundles on formal loops.
Corduneanu, Silvia-Otilia
Topologies on spaces of almost periodic measures
View Abstract Hide Abstract
Download the pdf of this abstract: Corduneanu Abstract
Croitoru, Anca
Convergence properties for sequences of measurable multifunctions
View Abstract Hide Abstract
In set-valued analysis, the theory of measurable multifunctions has numerous applications in statistics, mathematical economy, fixed point problems, optimization, theory of control, information systems or in modeling birth-and-growth processes. In this talk we present some convergence properties for sequences of measurable multifunctions and show that convergence in a monotone measure is equivalent to the convergence in a pseudo-metric.
Donald, Andrew
Embedding Seifert manifolds in the 4-sphere
View Abstract Hide Abstract
I will consider the question of which closed 3-manifolds can be smoothly embedded in 4-dimensional space. An obstruction can be derived from Donaldson's theorem on the intersection forms of smooth, closed 4-manifolds. This technique is useful when considering which rational homology spheres smoothly bound rational balls and, in this context, has recently been shown to be a powerful tool. It is particularly applicable to Seifert fibred 3-manifolds. In this talk I will discuss a few special cases of this embedding problem.
Friedl, Stefan
Fundamental groups of 3-manifolds
View Abstract Hide Abstract
We will give a survey of the properties of fundamental groups of 3-manifolds, with an emphasis on the consequences of the proof of the Geometrization Conjecture. We will also outline talk about several recent results and conjectures, which highlight the role of right angled Artin groups in the theory of 3-manifold groups.
Grant, Mark
On immersions in homology classes
View Abstract Hide Abstract
We give examples of mod 2 homology classes in closed manifolds which cannot be represented by an immersion of closed manifolds. This is joint work with András Szucs (Eotvos Lorand).
Hepworth, Richard
Configuration-spaces and higher categories
View Abstract Hide Abstract
There are many competing definitions of "weak n-category", and several of them invoke a category called "Theta-n". The definition of Theta-n is entirely algebraic, but I will explain how it naturally encodes geometric information about spaces of configurations in R^n. This is joint work with David Ayala.
Huettemann, Thomas
A toric finiteness criterion for chain complexes over Laurent rings
View Abstract Hide Abstract
Download the pdf of this abstract: Huettemann Abstract
Lahtinen, Anssi
String topology of classifying spaces
View Abstract Hide Abstract
As discovered by Chataur and Menichi, the homology of the free loop space of the classifying space of a compact Lie group enjoys a very rich algebraic structure: it is the value of the circle in a two-dimensional Homological Field Theory, a field theory where the operations are parametrized by homology classes of spaces of two-dimensional cobordisms. In this talk, I will discuss a novel construction of this field theory that improves on Chataur and Menichi's original construction in various ways: it enlarges the family of admissible Lie groups, extends the field theory from a closed theory to an open-closed one, and, most importantly, allows for the construction of co-units for the theory. This research is joint work in progress with Richard Hepworth.
Rasmussen, Jacob
Khovanov homology of torus knots
View Abstract Hide Abstract
Khovanov homology is an invariant of knots in S^3 which generalizes the Jones polynomial. It has many interesting geometrical properties, but in many respects is still poorly understood. In this talk I'll discuss some conjectures (joint with E. Gorsky, A. Oblomkov, and V. Shende) relating Khovanov homology of torus knots to algebraic geometry (Hilbert schemes of singular plane curves) and representation theory.
Schleimer, Saul
The structure theorem for train track splitting sequences.
View Abstract Hide Abstract
The structure theorem details how train track splitting sequences interact with subsurface projections to curve complexes. I will briefly describe the corresponding structure theorems for hierarchies (Masur-Minsky), Teichmuller geodesics (Rafi) and three-manifolds (Minsky, Bowditch). If time permits we will also discuss the recent work of Bestvina and Feighn, on folding paths in outer space and their projections to free factor complexes. This is joint work with Howie Masur and Lee Mosher.
Stroppel, Catharina
Categorification and fractional Euler characteristics
View Abstract Hide Abstract
I will explain the idea of categorification illustrated by some examples and introduce the notion of fractional Euler characteristics.
Tillmann, Ulrike
Homology stability for some families of diffeomorphisms of manifolds
View Abstract Hide Abstract
Homology stability of families of groups have played an important role in stable homotopy theory, K-theory, and more recently in the topological approach to the Mumford conjecture which computes the homology of the mapping class groups of large genus. This has lead to renewed interest in homology stability more generally, and in particularly of that of mapping class groups and diffeomorphism groups of manifolds. We will explain this context and prove homology stability for certain diffeomorphism groups of higher dimensional manifolds. In particular, we lift some of the results of Hatcher and Wahl for mapping class groups to the level of diffeomorphisms.
Turgay, Neset Deniz
Conjugation invariants in the dual Leibniz-Hopf algebra
View Abstract Hide Abstract
The Leibniz-Hopf algebra is the free associative algebra with one generator in each degree and co-product given by the Cartan formula. The mod 2 Steenrod algebra naturally occurs as a quotient of this Hopf algebra by the Adem relations. Several years ago, motivated by its link with commutativity of ring spectra, the first author and Sarah Whitehouse attempted to compute the invariants under conjugation in the dual Steenrod algebra. A complete calculation was not possible then, so we present a different approach to this problem. In particular, we calculate the conjugation invariants in the mod 2 dual Leibniz-Hopf algebra. Since the dual Steenrod algebra is a sub Hopf algebra of this algebra, so the conjugation invariants in the dual Steenrod algebra are the intersection of the Leibniz-Hopf conjugation invariants and the dual Steenrod algebra. We show that, like in the dual Steenrod algebra, the degree-wise dimension of the conjugation invariants is "approximately'" half that of the whole algebra. But the nature of the approximation in the two cases turns out to be somewhat different.
Vejdemo-Johansson, Mikael
Persistent cohomology and its applications
View Abstract Hide Abstract
In recent work, we have introduced the concept of persistent cohomology, and demonstrated how this can produce coordinate functions on point clouds with values on a circle. I shall describe this work, and some of the applications we have been able to find for these techniques in the analysis of periodic systems and signals.
Vogtmann, Karen
Hairy graphs and the cohomology of Out(F_n)
View Abstract Hide Abstract
Kontsevich showed that the homology of Out(F_n) can be identified with the cohomology of a certain Lie algebra A. Morita constructed cocycles from elements of the abelianization of A. We will show that the abelianization of A is strictly larger than Morita conjectured, then use the new information to construct new cocycles out of "hairy graphs". These include a heretofore mysterious unstable homology class in Aut(F_5) which was found in 2002 by F. Gerlits. This is joint work with Jim Conant and Martin Kassabov.
Wiemeler, Michael
Non-abelian Lie-groups acting on quasitoric manifolds.
View Abstract Hide Abstract
A quasitoric manifold is an 2n-dimensional manifold with a well-behaved action of an n-dimensional torus. In my talk I will discuss the following two questions: - When does the torus action on a quasitoric manifold extend to an action of a compact connected non-abelian Lie-group? - If there is such an action, is it unique?

Participants

Name	Institution
Adams-Florou, Spiros	University of Edinburgh
Al-Hajaj, Haitham	Swansea university
Aramayona, Javier	National University of Ireland at Galway
Baker, Andrew	University of Glasgow
Brendle, Tara	University of Glasgow
Cheung, Pokman	University of Sheffield
Corduneanu, Silvia-Otilia	Gh. Asachi Technical University of Iasi
Croitoru, Anca	"Al.I. Cuza" University of Iasi, Faculty of Mathematics
Crossley, Martin	Swansea University
Donald, Andrew	University of Glasgow
Friedl, Stefan	Universität zu Köln
Fullarton, Neil	University of Glasgow
Gilbert, Nick	Heriot-Watt University
Gordon, Iain	University of Edinburgh
Grant, Mark	University of Edinburgh
Hepworth, Richard	University of Aberdeen
Howie, Jim	Heriot-Watt University
Huettemann, Thomas	Queen's University Belfast
Lahtinen, Anssi	University of Copenhagen
Levikov, Filipp	University of Aberdeen
Orson, Patrick	University of Edinburgh
Owens, Brendan	University of Glasgow
Palmer, Chris	University of Edinburgh
Palmer, Martin	University of Oxford
Ranicki, Andrew	University of Edinburgh
Rasmussen, Jacob	University of Cambridge
Rodenhausen, Moritz	University of Oxford
Rovi, Ana	University of Glasgow
Rovi, Carmen	University of Edinburgh
Salchow, Jan-David	Humboldt University Berlin
Schleimer, Saul	University of Warwick
Schuetz, Dirk	Durham University
Singer, Michael	University College London
Stroppel, Catharina	University of Bonn
Tillmann, Ulrike	University of Oxford
Turgay, Neset Deniz	University of Wales, Swansea
Ullman, Harry	University of Sheffield
Vejdemo-Johansson, Mikael	University of St Andrews
Vogtmann, Karen	Cornell University
Wall, Terry	Univ of Liverpool
Wallis, Alistair	Heriot-Watt University
Wiemeler, Michael	University of Manchester