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.
"Homotopy algebra structures on twisted tensor products and string topology operations." Algebr. Geom. Topol. 11 (2) 1163 - 1203, 2011. https://doi.org/10.2140/agt.2011.11.1163