Tautological classes and smooth bundles over BSU(2)

Tautological classes and smooth bundles over BSU(2)

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...

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Veröffentlicht in:arXiv.org 2018-10
1. Verfasser: Reinhold, Jens
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Sprache:eng
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Bundles
Bundling
Homology
Lie groups
Manifolds
Mathematics - Algebraic Topology
Mathematics - Geometric Topology
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description 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.
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subjects Bundles
Bundling
Homology
Lie groups
Manifolds
Mathematics - Algebraic Topology
Mathematics - Geometric Topology
title Tautological classes and smooth bundles over BSU(2)
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