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 | References | Similar Articles | Additional Information

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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© Copyright 1995
American Mathematical Society