Abstract
We prove that a nilpotent space is both formal and coformal if and
only if it is rationally homotopy equivalent to the derived spatial realization
of a graded commutative Koszul algebra. We call such spaces Koszul spaces
and show that the rational homotopy groups and the rational homology of
iterated loop spaces of Koszul spaces can be computed by applying certain
Koszul duality constructions to the cohomology algebra.
only if it is rationally homotopy equivalent to the derived spatial realization
of a graded commutative Koszul algebra. We call such spaces Koszul spaces
and show that the rational homotopy groups and the rational homology of
iterated loop spaces of Koszul spaces can be computed by applying certain
Koszul duality constructions to the cohomology algebra.
| Originalsprog | Engelsk |
|---|---|
| Tidsskrift | Transactions of the American Mathematical Society |
| Vol/bind | 366 |
| Udgave nummer | 9 |
| Sider (fra-til) | 4551-4569 |
| ISSN | 0002-9947 |
| DOI | |
| Status | Udgivet - 2014 |