On the construction and the topological invariance of the Pontryagin classes

Andrew Ranicki, Michael Weiss

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

We use sheaves and algebraic L-theory to construct the rational Pontryagin classes of fiber bundles with euclidean space fibers. 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.
Original languageEnglish
Pages (from-to)309-343
Number of pages35
JournalGeometriae Dedicata
Volume148
Issue number1
Early online date18 Aug 2010
DOIs
Publication statusPublished - Oct 2010

Fingerprint

Invariance
Transversality
Fiber Bundle
Sheaves
Vector Bundle
Euclidean space
Torus
Fiber
Alternatives
Theorem
Class

Keywords

  • L-theory
  • characteristic classes
  • sheaves
  • Poincare duality

Cite this

On the construction and the topological invariance of the Pontryagin classes. / Ranicki, Andrew; Weiss, Michael.

In: Geometriae Dedicata, Vol. 148, No. 1, 10.2010, p. 309-343.

Research output: Contribution to journalArticle

Ranicki, Andrew ; Weiss, Michael. / On the construction and the topological invariance of the Pontryagin classes. In: Geometriae Dedicata. 2010 ; Vol. 148, No. 1. pp. 309-343.
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