|材料类型：||文献, 硕士论文/博士论文, 互联网资源|
Eric James Malm; Ralph L Cohen; G Carlsson; Søren Galatius; Steve Kerckhoff; Stanford University. Department of Mathematics.
|注意：||Submitted to the Department of Mathematics.|
|描述：||1 online resource.|
|责任：||Eric James Malm.|
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.