arXiv 0910.53672009-10math.GTmath.AT

Vanishing of universal characteristic classes for handlebody groups and boundary bundles

Jeffrey Giansiracusa, Ulrike Tillmann

备注：: 9 pages, final version to appear in JHRS

英文摘要：

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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