The loop homology algebra of spheres and projective spaces

dc.creatorCohen, Ralph L.
dc.creatorJones, John D. S
dc.creatorYan, Jun
dc.date2002-10-22
dc.date.accessioned2026-07-07T04:52:15Z
dc.date.available2026-07-07T04:52:15Z
dc.descriptionChas 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.description15 pages, 0 figures, to appear in Proc. of Alg. Topology, Conf., Isle of Skye, 2001
dc.identifierhttps://arxiv.org/abs/math/0210353
dc.identifierhttp://arxiv.org/abs/math/0210353
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/65399
dc.subjectAlgebraic Topology
dc.subject55T99; 57T99; 58D15
dc.titleThe loop homology algebra of spheres and projective spaces
dc.typetext

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