Cyclic theory for commutative differential graded algebras and s-cohomology
| dc.creator | Burghelea, Dan | |
| dc.date | 2009-05-10 | |
| dc.date.accessioned | 2026-07-07T13:13:36Z | |
| dc.date.available | 2026-07-07T13:13:36Z | |
| dc.description | In this paper one considers three homotopy functors on the category of manifolds, $hH^\ast, cH^\ast, sH^\ast,$ and parallel them with other three homotopy functors on the category of connected commutative differential graded algebras, $HH^\ast, CH^\ast, SH^\ast.$ If $P$ is a smooth 1-connected manifold and the algebra is the de-Rham algebra of $P$ the two pairs of functors agree but in general do not. The functors $ HH^\ast $ and $CH^\ast$ can be also derived as Hochschild resp. cyclic homology of commutative differential graded algebra, but this is not the way they are introduced here. The third $SH^\ast ,$ although inspired from negative cyclic homology, can not be identified with any sort of cyclic homology of any algebra. The functor $sH^\ast$ might play some role in topology. Important tools in the construction of the functors $HH^\ast, CH^\ast $and $SH^\ast ,$ in addition to the linear algebra suggested by cyclic theory, are Sullivan minimal model theorem and the "free loop" construction described in this paper. | |
| dc.identifier | https://arxiv.org/abs/0905.1489 | |
| dc.identifier | http://arxiv.org/abs/0905.1489 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/229941 | |
| dc.subject | Algebraic Topology | |
| dc.subject | K-Theory and Homology | |
| dc.subject | 57R20, 57R58, 57R70, 57Q10, 58J52 | |
| dc.title | Cyclic theory for commutative differential graded algebras and s-cohomology | |
| dc.type | text |