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Vanishing of universal characteristic classes for handlebody groups and boundary bundles

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Jeffrey Giansiracusa and Ulrike Tillmann

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 $B\Diff(\partial W)$ to $B\Diff(W)$.

Journal of Homotopy and Related Structures, Vol. 6(2011), No. 1, pp. 103-112