TY - ELEC
DB - /z-wcorg/
DP - http://worldcat.org
ID - 665049539
LA - English
UR - http://purl.stanford.edu/vs885hy7344
T1 - String topology and the based loop space
AU - Malm, Eric James.
AU - Cohen, Ralph L.,
AU - Carlsson, G.
AU - Galatius, Søren,
AU - Kerckhoff, Steve,
AU - Stanford University.
AU - Department of Mathematics.
Y1 - 2010///
AB - We relate the Batalin-Vilkovisky (BV) algebra structure of the string topology of a manifold to the homological algebra of the singular chains of the based loop space of that manifold, showing that its Hochschild cohomology carries a BV algebra structure isomorphic to that of string topology. Furthermore, this structure is compatible with the usual cup product and Lie bracket on Hochschild cohomology. This isomorphism arises from a derived form of Poincare duality using modules over the based loop space as local coefficient systems. This derived Poincare duality also comes from a form of fibrewise Atiyah duality on the level of fibrewise spectra, and we use this perspective to connect the algebraic constructions to the Chas-Sullivan loop product.
ER -