Algebraic & Geometric Topology
- Algebr. Geom. Topol.
- Volume 11, Number 2 (2011), 1163-1203.
Homotopy algebra structures on twisted tensor products and string topology operations
Given a coalgebra , a strict dg Hopf algebra and a twisting cochain such that , we describe a procedure for obtaining an coalgebra on . This is an extension of Brown’s work on twisted tensor products. We apply this procedure to obtain an coalgebra model of the chains on the free loop space based on the coalgebra structure of induced by the diagonal map and the Hopf algebra model of the based loop space given by . When has cyclic coalgebra structure, we describe an algebra on . This is used to give an explicit (nonminimal) algebra model of the string topology loop product. Finally, we discuss a representation of the loop product in principal –bundles.
Algebr. Geom. Topol., Volume 11, Number 2 (2011), 1163-1203.
Received: 14 June 2010
Revised: 31 January 2011
Accepted: 4 February 2011
First available in Project Euclid: 19 December 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 55P35: Loop spaces 55R99: None of the above, but in this section 57N65: Algebraic topology of manifolds 57R22: Topology of vector bundles and fiber bundles [See also 55Rxx] 57M99: None of the above, but in this section
Secondary: 55Q33 55Q32
Miller, Micah. Homotopy algebra structures on twisted tensor products and string topology operations. Algebr. Geom. Topol. 11 (2011), no. 2, 1163--1203. doi:10.2140/agt.2011.11.1163. https://projecteuclid.org/euclid.agt/1513715223