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2011 On the mapping space homotopy groups and the free loop space homology groups
Takahito Naito
Algebr. Geom. Topol. 11(4): 2369-2390 (2011). DOI: 10.2140/agt.2011.11.2369


Let X be a Poincaré duality space, Y a space and f:XY a based map. We show that the rational homotopy group of the connected component of the space of maps from X to Y containing f is contained in the rational homology group of a space LfY which is the pullback of f and the evaluation map from the free loop space LY to the space Y. As an application of the result, when X is a closed oriented manifold, we give a condition of a noncommutativity for the rational loop homology algebra H(LfY;) defined by Gruher and Salvatore which is the extension of the Chas–Sullivan loop homology algebra.


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Takahito Naito. "On the mapping space homotopy groups and the free loop space homology groups." Algebr. Geom. Topol. 11 (4) 2369 - 2390, 2011.


Received: 26 January 2011; Revised: 10 May 2011; Accepted: 10 July 2011; Published: 2011
First available in Project Euclid: 19 December 2017

zbMATH: 1237.55006
MathSciNet: MR2835233
Digital Object Identifier: 10.2140/agt.2011.11.2369

Primary: 55P35, 55P50
Secondary: 55P62

Rights: Copyright © 2011 Mathematical Sciences Publishers


Vol.11 • No. 4 • 2011
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