Bonn Topology Group - Abstracts
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Talk
Diarmuid Crowley (HIM Bonn): Some new calculations for the Gromoll filtration (17 May 2011)
Abstract
Let \Gamma_n denote the group of oriented homotopy n-spheres, n > 4. There
is a decreasing filtration of \Gamma_n due to Gromoll:
\Gamma = \Gamma_{n, 2} \supset \Gamma_{n, 3} \supset ... \supset \Gamma_{n, n-3} = 0
The determination of the Gromoll filtration is a difficult open problem (it seems to be
unknown for any n > 6, n \neq 12) which has many interesting applications in geometric
topology.
In this talk I will survey approaches to finding elements deeper in the Gromoll
filtration: plumbing and compostion and also obstructions to finding such elements
from pseudo-isotopy theory. Then I will report on new computations for certain
Gromoll groups. As time permits I will discuss applications and open problems.
Many of the new results are part of joint work with with Thomas Schick.
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