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Exotic Spheres 02

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

What
  • Topology Seminar
When Thu, Jan 28, 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.

 

Chirasree will do Items 5 & 6 from Lecture 01, thus completing a modern approach to Sections 1–2 of the paper.

 

OUTLINE for Gerrit Smith

  1. Definition of an abstract manifold being stably parallelizable; the standard n-sphere necessarily satisfies this property.
  2. Why stabilizing once was enough (Lemma 3.5); a survey of the machine from algebraic topology called obstruction theory.
  3. Why the notion in Item 1 is equivalent to parallelizable for manifolds-with-boundary (Lemma 3.4).
  4. An equivalent notion for embedded manifolds (Lemma 3.3).
  5. The three-case proof that any homotopy n-sphere is stably parallelizable (Theorem 3.1).  This is independent of Items 2–4, which were merely remarks on Item 1.

 

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