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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality 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 1.43.

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Homology operations on a new infinite loop space
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by Burt Totaro PDF
Trans. Amer. Math. Soc. 347 (1995), 99-110 Request permission

Abstract:

Boyer et al. [1] defined a new infinite loop space structure on the space ${M_0} = {\prod _{n \geqslant 1}}K({\mathbf {Z}},2n)$ such that the total Chern class map $BU \to {M_0}$ is an infinite loop map. This is a sort of Riemann-Roch theorem without denominators: for example, it implies Fulton-MacPherson’s theorem that the Chern classes of the direct image of a vector bundle $E$ under a given finite covering map are determined by the rank and Chern classes of $E$. We compute the Dyer-Lashof operations on the homology of ${M_0}$. They provide a new explanation for Kochman’s calculation of the operations on the homology of $BU$, and they suggest a possible characterization of the infinite loop structure on ${M_0}$.
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Additional Information
  • © Copyright 1995 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 347 (1995), 99-110
  • MSC: Primary 55S12; Secondary 55P47, 57T25
  • DOI: https://doi.org/10.1090/S0002-9947-1995-1273541-8
  • MathSciNet review: 1273541