Author: Andrey Lazarev
Title: Spaces of multiplicative maps between highly structured ring spectra.


We uncover a somewhat unexpected connection between spaces of multiplicative maps 
between 
A-infinity 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-infinity map
MU-->MU.  This implies, in particular, that the Brown-Peterson spectrum
BP splits off MU as an A-infinity ring spectrum.