On the construction and topological invariance of the Pontryagin classes
arXiv:0901.0819
Abstract
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.
arXiv comment32 pages. Submitted for publication. v2: minor revision, new references added