Abstract
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.
| Translated title of the contribution | Spaces of multiplicative maps between highly structured ring spectra |
|---|---|
| Original language | English |
| Title of host publication | Categorical Decomposition Techniques in Algebraic Topology, International Conference in Algebraic Topology, Isle of Skye, Scotland, June 2001 |
| Editors | Arone , G.; Hubbuck, J.; Levi, M R.; Weiss |
| Publisher | Birkhäuser Basel |
| Pages | 237 - 259 |
| Volume | 215 |
| ISBN (Print) | 3764304006 |
| Publication status | Published - 2004 |