Mapping space of unbounded differential graded algebras over a field

Speaker: 
Ilias Amrani
Monday, July 22, 2013 - from 16:30 to 16:55
Abstract: 
In this paper, we give a concrete description of the higher homotopy groups ($n>0$) of the mapping space $\mathrm{Map}_{\mathsf{dgAlg}_{k}}(R,S)$ for $R$ and $S$ unbounded differential graded algebras (DGA) over a field $k$. In the connective case, and for any square zero extension $R\oplus M$ of $R$ we describe the relation between the higher negative derivation groups $\mathrm{Der}_{k}^{-n}(R,M)$ and higher homotopy groups $\pi_{n}\mathrm{Map}_{\mathsf{dgAlg}_{k}}(R,R\oplus M)$, when $n>1$. These two groups differ by the (negative) Hochschild cohomology $\mathrm{HH}_{k}^{-n+1}(R).$