Journal article 554 views

Vanishing of universal characteristic classes for handlebody groups and boundary bundles / Jeff Giansiracusa; Ulrike Tillmann

Springer/TCMS, Volume: 6, Issue: 1, Pages: 103 - 112

Swansea University Author:

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 sp...

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Published in: Springer/TCMS 2011 https://cronfa.swan.ac.uk/Record/cronfa8377 No Tags, Be the first to tag this record!
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(\partial W) to BDiff(W). College of Science 1 103 112