Vanishing of universal characteristic classes for handlebody groups and boundary bundles

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).

9 pages, final version to appear in JHRS

References in corpus (3)

• Stabilization for mapping class groups of 3-manifolds
• Stable characteristic classes of smooth manifold bundles
• Cobordism categories of manifolds with corners

Cited by in corpus (1)

• Secondary characteristic classes for subgroups of automorphism groups of free groups