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
收藏
页码：2749 / 2781
页数：33
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