No abstract

Given a C∞ coalgebra C * , a strict dg Hopf algebra H * , and a twisting cochain τ : C * → H * such that Im(τ ) ⊂ P rim(H * ), we describe a procedure for obtaining an A∞ coalgebra on C * ⊗ H * . 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 M → M × 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 C * ⊗ H * . This is used to give an explicit (non-minimal) A∞ algebra model of the string topology loop product. Finally, we discuss a representation of the loop product in principal G-bundles.