## Exotic spheres

### V5D1 – Advanced Topics in Topology – Exotic spheres

Sommersemester 2017

Lectures: Tuesday 14:15 – 16:00, Wednesday 16:15 – 19:00

Room: Seminar room 0.007 (ground floor, Endenicher Allee 60)

Link to the official course webpage in basis.

Brief introduction.

Summary of the topics covered in the lectures.

Some more detailed notes for the first six lectures. (I did not keep up with typing up all of the notes during the lecture course, but I intend to type these up eventually – watch this space..!)

#### Exam

The exam for the course is an oral exam. The first round of exams took place on Monday-Tuesday of the final week of the semester, i.e. on the 24th and 25th of July. The second round of exams will take place on Monday-Tuesday 25th-26th September.

#### Literature

– Milnor (1956), On manifolds homeomorphic to the 7-sphere

– Milnor (1959), Differentiable structures on spheres

– Brown (1960), A proof of the generalized Schoenflies theorem

– Palais (1960), Extending diffeomorphisms

– Palais (1960), Local triviality of the restriction map for embeddings

– Kervaire-Milnor (1963), Groups of homotopy spheres: I

– Milnor (1965), Lectures on the h-cobordism theorem

– Phạm (1965), Formules de Picard-Lefschetz généralisées et ramification des intégrales

– Brieskorn (1966), Beispiele zur Differentialtopologie von Singularitäten

– Hirzebruch (1966/67), Singularities and exotic spheres

– Connell (1967), A topological h-cobordism theorem for n ≥ 5

– Milnor (1968), Singular points of complex hypersurfaces

– Browder (1972), Surgery on simply-connected manifolds

– Levine (1985), Lectures on groups of homotopy spheres

– Gompf (1985), An infinite set of exotic R^{4}s

– Lück (2002), A basic introduction to surgery theory

– Scorpan (2005), The wild world of 4-manifolds

– Joachim-Wraith (2008), Exotic spheres and curvature

– Andrew Ranicki’s webpage on exotic spheres

– Manifold Atlas page on exotic spheres

– Two expository articles by John Milnor:

– Fifty Years Ago: Topology of Manifolds in the 50’s and 60’s (2006)

– Differential Topology Forty-six Years Later (2011)