AN ALGEBRAIC CHAIN MODEL OF STRING TOPOLOGY

被引：3

作者：

Chen, Xiaojun ^{[1
,2
]}

机构：

[1] Sichuan Univ, Sch Math, Chengdu 610064, Peoples R China

[2] Univ Michigan, Dept Math, Ann Arbor, MI 48104 USA

来源：

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 2012年 / 364卷 / 05期

关键词：

String topology; free loop space; Batalin-Vilkovisky algebra; Gerstenhaber algebra; BATALIN-VILKOVISKY ALGEBRAS; COHOMOLOGY; OPERATIONS; HOMOLOGY;

D O I：

10.1090/S0002-9947-2011-05518-2

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A chain complex model for the free loop space of a connected, closed and oriented manifold is presented, and on its homology, the Gerstenhaber and Batalin-Vilkovisky algebra structures are defined and identified with the string topology structures. The gravity algebra on the equivariant homology of the free loop space is also modeled. The construction includes the non-simply connected case, and therefore gives an algebraic and chain level model of Chas-Sullivan's String Topology.

引用

页码：2749 / 2781

页数：33

共 43 条

[11] The homotopy invariance of the string topology loop product and string bracket [J].

Cohen, Ralph L. ;

Klein, John R. ;

Sullivan, Dennis .

JOURNAL OF TOPOLOGY, 2008, 1 (02) :391-408

[12] A homotopy theoretic realization of string topology [J].

Cohen, RL ;

Jones, JAS .

MATHEMATISCHE ANNALEN, 2002, 324 (04) :773-798

[13]

Connes A., 1985, PUBL MATH IHES, V62, P41

[14] Topological conformal field theories and Calabi-Yau categories [J].

Costello, Kevin .

ADVANCES IN MATHEMATICS, 2007, 210 (01) :165-214

[15]

Félix Y, 2007, J EUR MATH SOC, V9, P123

[16] RATIONAL BV-ALGEBRA IN STRING TOPOLOGY [J].

Felix, Yves ;

Thomas, Jean-Claude .

BULLETIN DE LA SOCIETE MATHEMATIQUE DE FRANCE, 2008, 136 (02) :311-327

[17] COHOMOLOGY STRUCTURE OF AN ASSOCIATIVE RING [J].

GERSTENHABER, M .

ANNALS OF MATHEMATICS, 1963, 78 (02) :267-&

[18] BATALIN-VILKOVISKY ALGEBRAS AND 2-DIMENSIONAL TOPOLOGICAL FIELD-THEORIES [J].

GETZLER, E .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1994, 159 (02) :265-285

[19] DIFFERENTIAL FORMS ON LOOP-SPACES AND THE CYCLIC BAR COMPLEX [J].

GETZLER, E ;

JONES, JDS ;

PETRACK, S .

TOPOLOGY, 1991, 30 (03) :339-371

[20] 2-DIMENSIONAL TOPOLOGICAL GRAVITY AND EQUIVARIANT COHOMOLOGY [J].

GETZLER, E .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1994, 163 (03) :473-489

← 1 2 3 4 5 →