Generalised Miller-Morita-Mumford classes for block bundles and topological bundles

Abstract

The most basic characteristic classes of smooth fibre bundles are the generalised Miller-Morita-Mumford classes, obtained by fibre integrating characteristic classes of the vertical tangent bundle. In this note we show that they may be defined for more general families of manifolds than smooth fibre bundles: smooth block bundles and topological fibre bundles.

18 pages

References in corpus (4)

• Homological stability for moduli spaces of high dimensional manifolds. I
• Homological stability for moduli spaces of high dimensional manifolds
• Torelli spaces of high-dimensional manifolds
• Stable moduli spaces of high dimensional manifolds

Cited by in corpus (14)

• Some finiteness results for groups of automorphisms of manifolds
• On the cohomology of Torelli groups
• The positive scalar curvature cobordism category
• A vanishing theorem for tautological classes of aspherical manifolds
• A homological approach to pseudoisotopy theory. I
• Relations among characteristic classes of manifold bundles
• Proving homological stability for homeomorphisms of manifolds
• An $H{P}^2$-bundle over $S^4$ with nontrivial $\hat{A}$-genus
• Tautological classes of definite 4-manifolds
• Bundle Transfer of L-Homology Orientation Classes for Singular Spaces
• A note on rational homological stability for automorphisms of manifolds
• The homology of moduli spaces of 4-manifolds may be infinitely generated
• Some rational homology computations for diffeomorphisms of odd-dimensional manifolds
• Mapping class groups of $h$-cobordant manifolds