From mapping class groups to automorphism groups of free groups

Details From mapping class groups to automorphism groups of free groups From mapping class groups to automorphism groups of free groups

2004-06-14

arxiv.org/abs/math/0406278v2

J. London Math. Soc. (2) 72 (2005) no. 2, 510-524

Mathematics

Algebraic Topology

to appear in J. Lond. Math. Soc

Scientific paper

We show that the natural map from the mapping class groups of surfaces to the
automorphism groups of free groups, induces an infinite loop map on the
classifying spaces of the stable groups after plus construction. The proof uses
automorphisms of free groups with boundaries which play the role of mapping
class groups of surfaces with several boundary components.

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