Tautological classes and smooth bundles over BSU(2)
Algebraic Topology
2020-11-24 v2 Geometric Topology
Abstract
For a Lie group G and a smooth manifold W, we study the difference between smooth actions of G on W and bundles over the classifying space of G with fiber W and structure group Diff(W). In particular, we exhibit smooth manifold bundles over BSU(2) that are not induced by an action. The main tool for reaching this goal is a technical result that gives a constraint for the values of tautological classes pulled back to the cohomology of BSU(2) along a map induced by an action.
Cite
@article{arxiv.1802.02248,
title = {Tautological classes and smooth bundles over BSU(2)},
author = {Jens Reinhold},
journal= {arXiv preprint arXiv:1802.02248},
year = {2020}
}
Comments
final version, to appear in Proceedings of the American Mathematical Society