
arXiv: math/0406593
We use the computational power of rational homotopy theory to provide an explicit cochain model for the loop product and the string bracket of a 1-connected closed manifold M . We prove that the loop homology of M is isomorphic to the Hochschild cohomology of the cochain algebra C^\ast(M) with coefficients in itself. Some explicit computations of the loop product and the string bracket are given.
55P35, 54N45,55N33,17A65,81T30,17B55, Radical theory (nonassociative rings and algebras), rational homotopy, String topology, Hochschild cohomology, free loop space, string homology, FOS: Mathematics, Algebraic Topology (math.AT), Products and intersections in homology and cohomology, Mathematics - Algebraic Topology, Loop spaces
55P35, 54N45,55N33,17A65,81T30,17B55, Radical theory (nonassociative rings and algebras), rational homotopy, String topology, Hochschild cohomology, free loop space, string homology, FOS: Mathematics, Algebraic Topology (math.AT), Products and intersections in homology and cohomology, Mathematics - Algebraic Topology, Loop spaces
| selected citations These citations are derived from selected sources. This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically). | 15 | |
| popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network. | Top 10% | |
| influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically). | Top 10% | |
| impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network. | Average |
