On the construction and topological invariance of the Pontryagin classes
Algebraic Topology
2010-02-24 v2 K-Theory and Homology
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.
Keywords
Cite
@article{arxiv.0901.0819,
title = {On the construction and topological invariance of the Pontryagin classes},
author = {Andrew Ranicki and Michael Weiss},
journal= {arXiv preprint arXiv:0901.0819},
year = {2010}
}
Comments
32 pages. Submitted for publication. v2: minor revision, new references added