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Exotic Spheres 07

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

What
  • Topology Seminar
When Thu, Mar 03, 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.

 

In the last lecture, we got as far as setting up a spectral sequence. This is to show the vanishing of the rational homology groups of the fiber F of the map S^m --> K(Z,m).  Today, we will do the calculation.

(This will finish Serre's argument that the stable homotopy groups of spheres are finite, for positive indices.  This fact is used by Kervaire--Milnor in their showing that the groups of homotopy spheres are finite.)

Afterward, time permitting, Professor Khan will review the construction of the Leray--Serre spectral sequence that was used.

 

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