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Combinatorial and Geometric Group Theory
May 5-10, 2006
Vanderbilt University
Nashville, TN, USA

Organizers
Goulnara Arzhantseva, Mike Mihalik, Denis Osin, Mark Sapir, Efim Zelmanov

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The ephemeral Morita classes
by
Karen Vogtmann
Cornell University
Coauthors: James Conant

There is a series of cocycles in the cohomology of the group of automorphisms of a free group (first discovered by S. Morita) which have an elementary description in terms of finite graphs. The first two of these give nontrivial cohomology classes, and it is conjectured that they are all nontrivial; on the other hand according to a recent result of S. Galatius all classes must be stably trivial. We show that a single application of the stabilization map Aut(Fn) to Aut(Fn+1) kills these classes, so that they in fact disappear immediately after they appear.

Date received: February 17, 2006

Copyright © 2006 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caqu-40.