Symplectic A_∞-algebras and string topology operations

2007/07/26 by Hamilton, Alastair, Lazarev, Andrey
#Algebraic Topology (math.AT) #FOS: Mathematics #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.0707.4003

Abstract

In this paper we establish the existence of certain structures on the ordinary and equivariant homology of the free loop space on a manifold or, more generally, a formal Poincaré duality space. These structures; namely the loop product, the loop bracket and the string bracket, were introduced and studied by Chas and Sullivan under the general heading `string topology'. Our method is based on obstruction theory for C_∞-algebras and rational homotopy theory. The resulting string topology operations are manifestly homotopy invariant.

Related

• Reduced symplectic homology and string topology
• Homotopy algebras and noncommutative geometry
• Algebraic string topology from the neighborhood of infinity
• String topology for complex projective spaces
• String topology and the based loop space