String Topology for Lie Groups
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String Topology for Lie Groups. / A. Hepworth, Richard.
In: Journal of Topology, Vol. 3, No. 2, 2010, p. 424-442.Research output: Contribution to journal › Journal article › Research › peer-review
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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 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.
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 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.
U2 - 10.1112/jtopol/jtq012
DO - 10.1112/jtopol/jtq012
M3 - Journal article
VL - 3
SP - 424
EP - 442
JO - Journal of Topology
JF - Journal of Topology
SN - 1753-8416
IS - 2
ER -
ID: 21543309