Introductory lectures on manifold topology: Exotic spheres


September 7, 2020 - September 18, 2020

Mauricio Bustamante (Cambridge)
Manuel Krannich (Cambridge)

One of the milestones in the study of high-dimensional manifolds is Milnor's discovery of exotic spheres (that is, smooth manifolds that are homeomorphic but not diffeomorphic to the standard sphere) [Mil56], and their classification in homotopy theoretical terms due to Kervaire and Milnor [KM63]. The goal of these lectures is to explain Milnor's construction of an exotic 7-sphere and Kervaire-Milnor's approach to the classification of these spheres in every dimension. Along the way, we will touch on several central techniques in manifold topology such as characteristic classes, bordism theory, and surgery.

This online mini-course is aimed at graduate students with interest in topology, geometry, and related areas.

All seminars below will begin at 15:00 BST.

Monday 7th September - Mauricio Bustamante (Cambridge),

Wednesday 9th September - Mauricio Bustamante (Cambridge)

Monday 14th September - Manuel Krannich (Cambridge)

Tuesday 15th Spetember - Mauricio Bustamante (Cambridge)

Wednesday 16th September - Manuel Krannich (Cambridge)

Friday 18th September - Manuel Krannich (Cambridge)


Prerequisites for participation are detailed here.

 

To register for this introductory lecture series please complete this form.

These introductory lectures are sponsored by the London Mathematical Society


This seminar series is supported as part of the ICMS/INI Online Mathematical Sciences Seminars.

References

[KM63] M.A. Kervaire and J.W. Milnor. Groups of homotopy spheres. I. Ann. of Math. (2), 77:504-537, 1963.
[Mil56] J. Milnor. On manifolds homeomorphic to the 7-sphere. Ann. of Math. (2), 64:399-405,1956.