Algebraic & Geometric Topology
- Algebr. Geom. Topol.
- Volume 11, Number 4 (2011), 2369-2390.
On the mapping space homotopy groups and the free loop space homology groups
Let be a Poincaré duality space, a space and a based map. We show that the rational homotopy group of the connected component of the space of maps from to containing is contained in the rational homology group of a space which is the pullback of and the evaluation map from the free loop space to the space . As an application of the result, when is a closed oriented manifold, we give a condition of a noncommutativity for the rational loop homology algebra defined by Gruher and Salvatore which is the extension of the Chas–Sullivan loop homology algebra.
Algebr. Geom. Topol., Volume 11, Number 4 (2011), 2369-2390.
Received: 26 January 2011
Revised: 10 May 2011
Accepted: 10 July 2011
First available in Project Euclid: 19 December 2017
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Naito, Takahito. On the mapping space homotopy groups and the free loop space homology groups. Algebr. Geom. Topol. 11 (2011), no. 4, 2369--2390. doi:10.2140/agt.2011.11.2369. https://projecteuclid.org/euclid.agt/1513715272