Spaces of multiplicative maps between highly structured ring spectra

Details Spaces of multiplicative maps between highly structured ring spectra Spaces of multiplicative maps between highly structured ring spectra

2002-09-27

arxiv.org/abs/math/0209388v1

Mathematics

Algebraic Topology

Scientific paper

We uncover a somewhat surprising connection between spaces of multiplicative maps between $A_\infty$-ring spectra and topological Hochschild cohomology. As a consequence we show that such spaces become infinite loop spaces after looping only once. We also prove that any multiplicative cohomology operation in complex cobordisms theory $MU$ canonically lifts to an $A_\infty$-map $MU\to MU$. This implies, in particular, that the Brown-Peterson spectrum $BP$ splits off $MU$ as an $A_\infty$-ring spectrum.

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