On the construction and topological invariance of the Pontryagin classes

Details On the construction and topological invariance of the Pontryagin classes On the construction and topological invariance of the Pontryagin classes

2009-01-07

arxiv.org/abs/0901.0819v2

Mathematics

Algebraic Topology

32 pages. Submitted for publication. v2: minor revision, new references added

Scientific paper

We use sheaves and algebraic L-theory to construct the rational Pontryagin
classes of fiber bundles with fiber R^n. This amounts to an alternative proof
of Novikov's theorem on the topological invariance of the rational Pontryagin
classes of vector bundles. Transversality arguments and torus tricks are
avoided.

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