Vanishing of universal characteristic classes for handlebody groups and boundary bundles

Details Vanishing of universal characteristic classes for handlebody groups and boundary bundles Vanishing of universal characteristic classes for handlebody groups and boundary bundles

2009-10-28

arxiv.org/abs/0910.5367v2

Mathematics

Geometric Topology

9 pages, final version to appear in JHRS

Scientific paper

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).

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