Floer homology of cotangent bundles and the loop product

Abbondandolo, Alberto¹ ; Schwarz, Matthias²

¹ Dipartimento di Matematica, Universita di Pisa, Largo Bruno Pontecorvo 5, 56127 Pisa, Italy
² Universität Leipzig, Mathematisches Institut, Postfach 10 09 20, D-04009 Leipzig, Germany

Geometry & topology, Tome 14 (2010) no. 3, pp. 1569-1722.

Résumé

We prove that the pair-of-pants product on the Floer homology of the cotangent bundle of a compact manifold $M$ corresponds to the Chas–Sullivan loop product on the singular homology of the loop space of $M$. We also prove related results concerning the Floer homological interpretation of the Pontrjagin product and of the Serre fibration. The techniques include a Fredholm theory for Cauchy–Riemann operators with jumping Lagrangian boundary conditions of conormal type, and a new cobordism argument replacing the standard gluing technique.

Détail

DOI : 10.2140/gt.2010.14.1569

Keywords: Floer homology, string topology, cotangent bundles, loop product

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