Abstract
The string coproduct is a coproduct on the homology with field coefficients of the free loop space of a closed oriented manifold introduced by Sullivan in string topology. The coproduct and the Chas-Sullivan loop product give an infinitesimal bialgebra structure on the homology if the Euler characteristic is zero. The aim of this paper is to study the string coproduct using Sullivan models in rational homotopy theory. In particular, we give a rational model for the string coproduct of pure manifolds. Moreover, we study the behavior of the string coproduct in terms of the Hodge decomposition of the rational cohomology of the free loop space. We also give computational examples of the coproduct rationally.
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Acknowledgements
We would like to thank the referees for reading our work carefully and providing many valuable suggestions. This work was supported by JSPS KAKENHI Grant Number JP18K13403.
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Communicated by Geoffrey Powell.
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Naito, T. Rational model for the string coproduct of pure manifolds. J. Homotopy Relat. Struct. 16, 667–702 (2021). https://doi.org/10.1007/s40062-021-00293-5
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DOI: https://doi.org/10.1007/s40062-021-00293-5