Vector bundles and projective modules

Research output: Contribution to journalArticle

10 Citations (Scopus)

Abstract

Serre and Swan showed that the category of vector bundles over a compact space X is equivalent to the category of finitely generated projective modules over the ring of continuous functions on X. In this paper, titled after the famous paper by Swan, this result is extended to an arbitrary topological space X. Also the well-known homotopy classification of the vector bundles over compact X up to isomorphism is extended to arbitrary X. It is shown that the Ko-functor and the Witt group of the ring of continuous functions on X coincide, and they are homotopy-type invariants of X.

Original languageEnglish (US)
Pages (from-to)749-755
Number of pages7
JournalTransactions of the American Mathematical Society
Volume294
Issue number2
DOIs
StatePublished - Jan 1 1986

Fingerprint

Rings of Continuous Functions
Projective Module
Vector Bundle
Witt Group
Homotopy Type
Arbitrary
Compact Space
Topological space
Functor
Homotopy
Finitely Generated
Isomorphism
Invariant

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

Cite this

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Vector bundles and projective modules. / Vaserstein, Leonid N.

In: Transactions of the American Mathematical Society, Vol. 294, No. 2, 01.01.1986, p. 749-755.

Research output: Contribution to journalArticle

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