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Transactions of the American Mathematical Society

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

 

 

Homology operations on a new infinite loop space


Author: Burt Totaro
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
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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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DOI: https://doi.org/10.1090/S0002-9947-1995-1273541-8
Article copyright: © Copyright 1995 American Mathematical Society