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Fall 2002 Midwest Topology Seminar

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November 2, 2002

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NATHALIE WAHL: GRAPHS, SURFACES, AUTOMORPHISMS OF FREE GROUPS, AND
MAPPING CLASS GROUPS

By considering the action on the fundamental group of a surface
(with at least one hole), we get a map from the mapping class group of
the surface to the automorphism group of the relevant free group.
We show that this map induces an infinite loop map on the classifying spaces
of the stable groups (after plus-construction). This is done by constructing
an appropriate operad with the automorphisms of free groups (using graphs).
This operad is a new example of an infinite loop space operad which is
not E_\infty.

*Last modified: October 9, 2002*