A Homotopy Theoretic Proof of the BV Identity in Loop Homology - Mathematics > Algebraic TopologyReportar como inadecuado




A Homotopy Theoretic Proof of the BV Identity in Loop Homology - Mathematics > Algebraic Topology - Descarga este documento en PDF. Documentación en PDF para descargar gratis. Disponible también para leer online.

Abstract: Chas and Sullivan proved the existence of a Batalin-Vilkovisky algebrastructure in the homology of free loop spaces on closed finite dimensionalsmooth manifolds using chains and chain homotopies. This algebraic structureinvolves an associative product called the loop product, a Lie bracket calledthe loop bracket, and a square 0 operator called the BV operator. Cohen andJones gave a homotopy theoretic description of the loop product in terms ofspectra. In this paper, we give an explicit homotopy theoretic description ofthe loop bracket and, using this description, we give a homological proof ofthe BV identity connecting the loop product, the loop bracket, and the BVoperator. The proof is based on an observation that the loop bracket and the BVderivation are given by the same cycle in the free loop space, except that theydiffer by parametrization of loops.



Autor: Hirotaka Tamanoi

Fuente: https://arxiv.org/







Documentos relacionados