Outer authomorphisms and the Jacobian

2005/02/13 by Kiyoshi Igusa, Igusa, Kiyoshi, John Klein +4
Mathematics · #55R40 #57M15 #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT) #math.KT #msc:55R40 #msc:57M15

paper · pdf · doi:10.48550/arxiv.math/0502266

19 pages, 2 figures

arxiv created 2005/02/13 · openalex publication_date 2005/02/13 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A graphs of rank n (homotopy equivalent to a wedge of n circles) without ``separating edges'' has a canonical n-dimensional compact C¹ 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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