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

TL;DR

This paper extends the definition of Miller-Morita-Mumford classes, fundamental characteristic classes in smooth fibre bundles, to more general families including block and topological bundles, broadening their applicability.

Contribution

It introduces a way to define Miller-Morita-Mumford classes for block and topological bundles, not just smooth fibre bundles, expanding the scope of these characteristic classes.

Findings

Miller-Morita-Mumford classes can be defined for block bundles.

Extension of classes to topological bundles is possible.

Broader applicability of characteristic classes in bundle theory.

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.