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Exotic Spheres 01

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

  • Topology Seminar
When Thu, Jan 21, 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.


OUTLINE for Chirasree Chatterjee

  1. Definition of homotopy n-sphere Σ.
  2. Examples given by clutching diffeomorphisms.
  3. Alternative definition of the commutative monoid Θn of homotopy n-spheres, which is simpler than that given in Sections 1–2.
  4. Existence of representation by clutching (n ⩾ 6); relation to the mapping class group of the standard (n-1)-sphere.
  5. Show that reversing orientation of Σ represents an inverse in Θn, using clutching.
  6. The two definitions of the commutative monoids Θn agree in dimension n ⩾ 5, using the h-cobordism theorem.


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