String Topology for Lie Groups

Abstract

In 1999 Chas and Sullivan showed that the homology of the free loop space of an oriented manifold admits the structure of a Batalin-Vilkovisky algebra. In this paper we give a direct description of this Batalin-Vilkovisky algebra in the case that the manifold is a compact Lie group G. Our answer is phrased in terms of the homology of G, the homology of the space of based loops on G, and the homology suspension. The result is applied to compute the Batalin-Vilkovisky algebra associated to the special orthogonal groups SO(n) with coefficients in the rational numbers and in the integers modulo two.

22 pages

References in corpus (3)

• Higher string topology operations
• The string topology BV algebra, Hochschild cohomology and the Goldman bracket on surfaces
• A Batalin-Vilkovisky Algebra structure on the Hochschild Cohomology of Truncated Polynomials

Cited by in corpus (12)

• String topology for complex projective spaces
• Higher operations in string topology of classifying spaces
• The bv algebra in string topology of classifying spaces
• Loop homology of quaternionic projective spaces
• The cohomology of free loop spaces of homogeneous spaces
• A reduction of the string bracket to the loop product
• Loop homology of some global quotient orbifolds
• Homotopy Algebra Structures on Twisted Tensor Products and String Topology Operations
• A Batalin-Vilkovisky algebra morphism from double loop spaces to free loops
• Behavior of the Eilenberg-Moore spectral sequence in derived string topology
• Integral String Lie Algebra Structure of Spheres
• String Homology and Lie Algebra Structures (Ph.D. Thesis)