Year: 2011
Type: article
Abstract: Given a C 1 coalgebra C , a strict dg Hopf algebra H and a twisting cochain W C ! H such that Im. / Prim.H /, we describe a procedure for obtaining an A 1 coalgebra on C ˝H .This is an extension of Brown's work on twisted tensor products.We apply this procedure to obtain an A 1 coalgebra model of the chains on the free loop space LM based on the C 1 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 /Œ 1/.When C has cyclic C 1 coalgebra structure, we describe an A 1 algebra on C ˝H .This is used to give an explicit (nonminimal) A 1 algebra model of the string topology loop product.Finally, we discuss a representation of the loop product in principal G -bundles.
Source: Algebraic & Geometric Topology
Author: Micah Miller
Institution: The Graduate Center, CUNY
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
OpenAlex ID: W1987526538