Open Access
Translator Disclaimer
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.


Download Citation

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

Keywords: free loop space , Hochschild (co)homology , mapping space , Rational homotopy theory , string topology

Rights: Copyright © 2011 Mathematical Sciences Publishers


Vol.11 • No. 4 • 2011
Back to Top