Detecting and realising characteristic classes of manifold bundles
Soren Galatius, Oscar Randal-Williams

TL;DR
This paper explores the non-triviality and dependence of characteristic classes in manifold bundles, extending the higher-dimensional Mumford conjecture and analyzing how these classes relate to characteristic numbers of fibers, total spaces, and bases.
Contribution
It applies advanced theoretical work to prove non-triviality of characteristic classes and investigates their dependence on characteristic numbers, advancing understanding in manifold bundle topology.
Findings
Proved non-triviality of certain characteristic classes
Analyzed dependence of classes on characteristic numbers
Extended higher-dimensional Mumford conjecture insights
Abstract
We apply our earlier work on the higher-dimensional analogue of the Mumford conjecture to two questions. Inspired by work of Ebert we prove non-triviality of certain characteristic classes of bundles of smooth closed manifolds. Inspired by work of Church-Farb-Thibault and Church-Crossley-Giansiracusa we investigate the dependence of characteristic classes of bundles on characteristic numbers of its fibre, total space and base space.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Geometry and complex manifolds · Homotopy and Cohomology in Algebraic Topology
