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Exotic Spheres 05

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Open to the public, a learning seminar with talks from advanced graduate students.

  • Topology Seminar
When Thu, Feb 18, 2016
from 11:00 AM to 12:00 PM
Where 202 Ritter Hall
Contact Name
Attendees rotating presentations by: Chirasree Chatterjee, Sean Corrigan, Gerrit Smith.
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The primary source is the seminal 1963 differential-topology article, "Groups of homotopy spheres," by Michel Kervaire and John Milnor.

Sean will present Section 4.  The goal is to prove Theorem 4.1:  For any fixed n > 4, there are only finitely many equivalence classes of homotopy n-spheres, where the equivalence relation is diffeomorphism up to connected sum with those special ones that bound a parallelizable (n+1)-manifold.

The seminar's goal is to show a version of Theorem 1.2:  For any fixed n>4, there are only finitely many diffeomorphism classes of homotopy n-spheres.  (That is, by the generalized PoincarĂ© theorem, there are only finitely many smooth structures on the standard n-sphere.)  Thus Theorem 4.1 reduces us to show that there are only finitely many possibilities for the 'special ones.'

(For continuity, here's a link to the previous talk.)


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