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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

An algebraic chain model of string topology


Author: Xiaojun Chen
Journal: Trans. Amer. Math. Soc. 364 (2012), 2749-2781
MSC (2010): Primary 55P50, 55P35
Published electronically: November 9, 2011
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Abstract: A chain complex model for the free loop space of a connected, closed and oriented manifold is presented, and on its homology, the Gerstenhaber and Batalin-Vilkovisky algebra structures are defined and identified with the string topology structures. The gravity algebra on the equivariant homology of the free loop space is also modeled. The construction includes the non-simply connected case, and therefore gives an algebraic and chain level model of Chas-Sullivan's String Topology.


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Additional Information

Xiaojun Chen
Affiliation: School of Mathematics, Sichuan University, Chengdu 610064, People’s Republic of China – and – Department of Mathematics, University of Michigan, 530 Church Street, Ann Arbor, Michigan 48104
Email: xch@umich.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-2011-05518-2
PII: S 0002-9947(2011)05518-2
Keywords: String topology, free loop space, Batalin-Vilkovisky algebra, Gerstenhaber algebra
Received by editor(s): February 25, 2010
Received by editor(s) in revised form: October 16, 2010, and November 13, 2010
Published electronically: November 9, 2011
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.