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Rational cohomology of the free loop space of a simply connected 4-manifold

  • A. Yu. Onishchenko
  • Th. Yu. PopelenskyEmail author
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Abstract

The purpose of this paper is to calculate the rational cohomology \({H^{\ast}(X^{{S}^{1}} ; \mathbb{Q})}\) of the free loop space for a simply connected closed 4-manifold X. We use minimal models, so the starting point is the cohomology algebra \({H^{\ast}(X; \mathbb{Q})}\) which depends only on the second Betti number b 2 and the signature of X itself. Calculations of \({H^{\ast}(X^{{S}^{1}} ; \mathbb{Q})}\) for b 2 ≤ 2 are known. We study the case b 2 > 2. We obtain an explicit formula for Poincaré series of the space \({X^{{S}^{1}}}\), with the second Betti number b 2 as a parameter.

Mathematics Subject Classification

55R20 55T35 55P50 55P62 

Keywords

Free loop space spectral sequence rational homology Sullivan model 
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© Springer Basel 2013

Authors and Affiliations

  1. 1.Faculty of Mechanics and MathematicsMoscow State University (MSU)Leninskie GoryRussia

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