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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Algebraic fiber bundles
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by Steven E. Landsburg PDF
Trans. Amer. Math. Soc. 266 (1981), 259-273 Request permission

Abstract:

When $X$ is a finite simplicial complex and $G$ is any of a certain class of groups, a classification of $G$-principal bundles over $X$ in terms of projective modules over a ring $R(G,X)$ is given. This generalizes Swan’s classification of vector bundles and uses the results of Mulvey. Often, $R$ can be taken to be noetherian; in this case ${\text {Spec}}(R)$ is usually reducible with "cohomologically trivial" irreducible components. Information is derived concerning the nature of projective modules over such rings, and some results are obtained indicating how such information reflects information about $X$.
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Additional Information
  • © Copyright 1981 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 266 (1981), 259-273
  • MSC: Primary 14F05; Secondary 13C10, 16A50, 55R25
  • DOI: https://doi.org/10.1090/S0002-9947-1981-0613795-1
  • MathSciNet review: 613795