Vanishing of universal characteristic classes for handlebody groups and boundary bundles

2009/10/28 by Jeffrey Giansiracusa, Giansiracusa, Jeffrey, Ulrike Tillmann +1
Mathematics · #57R20 #57R50 #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.0910.5367

openalex publication_date 2009/10/28 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

Using certain Thom spectra appearing in the study of cobordism categories, we show that the odd half of the Miller-Morita-Mumford classes on the mappping class group of a surface with negative Euler characteristic vanish in integral cohomology when restricted to the handlebody subgroup. This is a special case of a more general theorem valid in all dimensions: universal characteristic classes made from monomials in the Pontrjagin classes (and even powers of the Euler class) vanish when pulled back from BDiff(∂ W) to BDiff(W).

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