Homology, Homotopy and Applications

Volume 16 (2014)

Number 1

Homology operations and cosimplicial iterated loop spaces

Pages: 1 – 25

DOI: http://dx.doi.org/10.4310/HHA.2014.v16.n1.a1

Author

Philip Hackney (Department of Mathematics, University of California at Riverside)

Abstract

If $X$ is a cosimplical $E_{n+1}$ space then $\operatorname{Tot}(X)$ is an $E_{n+1}$ space and its mod 2 homology $H_*(\operatorname{Tot}(X))$ has Dyer-Lashof and Browder operations. It’s natural to ask if the spectral sequence converging to $H_*(\operatorname{Tot}(X))$ admits compatible operations. In this paper we give a positive answer to this question.

Keywords

Araki-Kudo operation, Browder operation, Dyer-Lashof operation, cosimplicial space, spectral sequence

2010 Mathematics Subject Classification

55S12, 55T20

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