String Topology for Lie Groups

TY - JOUR

T1 - String Topology for Lie Groups

AU - A. Hepworth, Richard

N1 - Keywords: math.AT; math.GT; 57R19, 58D99, 57T10

PY - 2010

Y1 - 2010

N2 - 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 where 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 mod 2.

AB - 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 where 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 mod 2.

U2 - 10.1112/jtopol/jtq012

DO - 10.1112/jtopol/jtq012

M3 - Journal article

SN - 1753-8416

VL - 3

SP - 424

EP - 442

JO - Journal of Topology

JF - Journal of Topology

IS - 2

ER -