Outer authomorphisms and the Jacobian

Details Outer authomorphisms and the Jacobian Outer authomorphisms and the Jacobian

2005-02-13

arxiv.org/abs/math/0502266v1

Mathematics

K-Theory and Homology

19 pages, 2 figures

Scientific paper

A graphs of rank n (homotopy equivalent to a wedge of n circles) without ``separating edges'' has a canonical n-dimensional compact C^1 manifold thickening. This implies that the canonical homomorphism f:Out(F_n)-> GL(n,Z) is trivial in rational cohomology in the stable range answering a question raised by Hatcher and Vogtmann [6]. Another consequence of the construction is the existence of higher Reidemeister torsion invariants for IOut(F_n)=ker f. These facts were first proved by the first author in [8] using different methods.

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