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

2013/06/30 by Johannes Ebert, Oscar Randal-Williams, Oscar Randal‐Williams · 2 citations
Mathematics · #Algebraic Geometry and Number Theory #Block (permutation group theory) #Bundle #Characteristic class #Chern class #Chern–Weil homomorphism #Cohomology #Combinatorics #Composite material #De Rham cohomology #Equivariant cohomology #Fiber bundle #Geometry #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology #Mathematics #Parallelizable manifold #Pure mathematics #Splitting principle #Tangent #Tangent bundle #Tangent space #Topology (electrical circuits) #Vector bundle #math.AT #msc:55R20 #msc:55R35 #msc:55R40 #msc:55R60 #msc:57N55 #msc:57R20 #msc:57R65 #msc:57S05

paper · pdf · doi:10.2140/agt.2014.14.1181

published as Algebr. Geom. Topol. 14 (2014) 1181-1204 · 18 pages

openalex publication_date 2014/03/21 · arxiv created 2015/01/29 · arxiv updated 2015/01/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

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.

Citations

• Singular homology groups and homotopy groups of finite topological spaces
• Stable moduli spaces of high dimensional manifolds
• On Spaces Having the Homotopy Type of a CW-Complex
• Homological stability for moduli spaces of high dimensional manifolds
• Topological Methods in Algebraic Geometry

Cited by

• A homological approach to pseudoisotopy theory. I
• Relations among characteristic classes of manifold bundles