The mapping space of unbounded differential graded algebras

Abstract

In this paper, we give a concrete description of the higher homotopy groups (n>0) of the mapping space Map_{Alg}(R,S) for R and S unbounded differential graded algebras (DGA) over a commutative ring k. In the connective case, we describe the relation between the higher (negative) Hochschild cohomology $H{H}^{-n+1}(R,S)$ and higher homotopy groups ${\pi }_{n}Ma{p}_{Alg}(R,S)$, when $n>1$.

We extend our previous results to any ground commutative ring k