Abstract
Let M be a smooth, simply-connected, closed oriented manifold, and LM the free loop space of M. Using a Poincaré duality model for M, we show that the reduced equivariant homology of LM has the structure of a Lie bialgebra, and we construct a Hopf algebra which quantizes the Lie bialgebra.
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Acknowledgements
The first author would like to thank Professor Yongbin Ruan for his encouragement during the preparation of this paper. The third author was partially supported by NSF grant DMS-0726154.
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Communicated by Y. Kawahigashi
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Chen, X., Eshmatov, F. & Gan, W.L. Quantization of the Lie Bialgebra of String Topology. Commun. Math. Phys. 301, 37–53 (2011). https://doi.org/10.1007/s00220-010-1139-z
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DOI: https://doi.org/10.1007/s00220-010-1139-z