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2011 Homotopy algebra structures on twisted tensor products and string topology operations
Micah Miller
Algebr. Geom. Topol. 11(2): 1163-1203 (2011). DOI: 10.2140/agt.2011.11.1163


Given a C coalgebra C, a strict dg Hopf algebra H and a twisting cochain τ:CH such that Im(τ) Prim(H), we describe a procedure for obtaining an A coalgebra on CH. This is an extension of Brown’s work on twisted tensor products. We apply this procedure to obtain an A coalgebra model of the chains on the free loop space LM based on the C coalgebra structure of H(M) induced by the diagonal map MM×M and the Hopf algebra model of the based loop space given by T(H(M)[1]). When C has cyclic C coalgebra structure, we describe an A algebra on CH. This is used to give an explicit (nonminimal) A algebra model of the string topology loop product. Finally, we discuss a representation of the loop product in principal G–bundles.


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Micah Miller. "Homotopy algebra structures on twisted tensor products and string topology operations." Algebr. Geom. Topol. 11 (2) 1163 - 1203, 2011.


Received: 14 June 2010; Revised: 31 January 2011; Accepted: 4 February 2011; Published: 2011
First available in Project Euclid: 19 December 2017

zbMATH: 1220.55005
MathSciNet: MR2792377
Digital Object Identifier: 10.2140/agt.2011.11.1163

Primary: 55P35, 55R99, 57M99, 57N65, 57R22
Secondary: 55Q32, 55Q33

Rights: Copyright © 2011 Mathematical Sciences Publishers


Vol.11 • No. 2 • 2011
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