Brackets in the Pontryagin algebras of manifolds
Brackets in the Pontryagin algebras of manifolds
复制标题
流形庞特里亚金代数中的括号
DOI：
--
复制
发表时间：
2013
期刊：
影响因子：
--
通讯作者：
V. Turaev
中科院分区：
文献类型：
--
作者：
G. Massuyeau;V. Turaev
Given a smooth oriented manifold $M$ with non-empty boundary, we study the Pontryagin algebra $A=H_ast(Omega )$ where $ Omega $ is the space of loops in $M$ based at a distinguished point of $ partial M$. Using the ideas of string topology of Chas-Sullivan, we define a linear map ${{-,-}}: A otimes A o Aotimes A$ which is a double bracket in the sense of Van den Bergh satisfying a version of the Jacobi identity. For $dim(M)geq 3$, the double bracket ${{-,-}}$ induces Gerstenhaber brackets in the representation algebras associated with $A$. This extends our previous work on the case $dim(M)=2$ where $A= H_0(Omega )$ is the group algebra of the fundamental group $pi_1(M)$ and the double bracket ${{-,-}}$ induces the standard Poisson brackets on the moduli spaces of representations of $pi_1(M)$.
在有角的流形上
DOI：
10.48550/arxiv.0910.3518
发表时间：
2009
期刊：
arXiv e-prints
影响因子：
--
作者：
Joyce Dominic
通讯作者：
Joyce Dominic