The loop homology algebra of spheres and projective spaces
| dc.creator | Cohen, Ralph L. | |
| dc.creator | Jones, John D. S | |
| dc.creator | Yan, Jun | |
| dc.date | 2002-10-22 | |
| dc.date.accessioned | 2026-07-07T04:52:15Z | |
| dc.date.available | 2026-07-07T04:52:15Z | |
| dc.description | Chas and Sullivan recently defined an intersection product on the homology $H_*(LM)$ of the space of smooth loops in a closed, oriented manifold $M$. In this paper we will use the homotopy theoretic realization of this product described by the first two authors to construct a second quadrant spectral sequence of algebras converging to the loop homology multiplicatively, when $M$ is simply connected. The $E_2$ term of this spectral sequence is $H^*(M;H_*(ΩM))$ where the product is given by the cup product on the cohomology of the manifold $H^* (M)$ with coefficients in the Pontryagin ring structure on the homology of its based loop space $H_*(ΩM)$. We then use this spectral sequence to compute the ring structures of $H_* (LS^n)$ and $H_* (L\bcp^n)$. | |
| dc.description | 15 pages, 0 figures, to appear in Proc. of Alg. Topology, Conf., Isle of Skye, 2001 | |
| dc.identifier | https://arxiv.org/abs/math/0210353 | |
| dc.identifier | http://arxiv.org/abs/math/0210353 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/65399 | |
| dc.subject | Algebraic Topology | |
| dc.subject | 55T99; 57T99; 58D15 | |
| dc.title | The loop homology algebra of spheres and projective spaces | |
| dc.type | text |