2010
665049539
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.
String topology and the based loop space
665049539
2010
en
2016-07-15
Galatius
Søren
Søren Galatius
1976
Malm
Eric James
Eric James Malm
Stanford University. Department of Mathematics.
Carlsson
G.
Gunnar
Gunnar Carlsson
1952
Kerckhoff
Steve
Steve Kerckhoff
Cohen
Ralph L.
Ralph L. Cohen
1952