The symplectic Verlinde algebras and string K-theory

辛群的积分弦拓扑与紧李群的BV刚性

BV rigidity for compact Lie groups and the integral string topology of the symplectic group

本文计算辛群自由环路空间的积分BV代数，并证明紧李群的环路空间BV代数由指数和基本群挠部分决定，单连通时等价于庞加莱对偶诱导的Hochschild上同调。

减少的辛同调与弦拓扑

Reduced symplectic homology and string topology

本文引入了循环积和循环余积的共同定义域——减少的循环同调，构建了幺半反交换双代数结构。并验证了Sullivan的猜想，通过二次持续映射的选择实现。

Symplectic $A_\infty$-algebras and string topology operations

In this paper we establish the existence of certain structures on the ordinary and equivariant homology of the free loop space on a manifold or, more generally, a formal Poincaré duality space. These structures; namely the loop product, the loop bracket and the string bracket, were introduced and studied by Chas and Sullivan under the general heading `string topology'. Our method is based on obstruction theory for $C_\infty$-algebras and rational homotopy theory. The resulting string topology operations are manifestly homotopy invariant.

BV双代数结构在Floer理论与弦拓扑中的应用

BV bialgebra structures in Floer theory and string topology

本文从模空间紧化拓扑导出BV双代数结构，并构造于约化辛同调、Rabinowitz Floer同调及非等变弦拓扑，同时展示等变情形下Lie双代数结构的形式推论。

Lie bialgebras and the cyclic homology of $A_\infty$ structures in topology

$A_\infty$ categories are a mathematical structure that appears in topological field theory, string topology, and symplectic topology. This paper studies the cyclic homology of a Calabi-Yau $A_\infty$ category, and shows that it is naturally an equivariant topological conformal field theory, and in particular, contains an involutive Lie bialgebra. Applications of the theory to string topology and the Fukaya category are given; in particular, it is shown that there is a Lie bialgebra homomorphism from the cyclic cohomology of the Fukaya category of a symplectic manifold with contact type bounda…

Topological quantum field theory structure on symplectic cohomology

We construct the TQFT on symplectic cohomology and wrapped Floer cohomology, possibly twisted by a local system of coefficients, and prove that the TQFT respects Viterbo restriction maps and the canonical maps from ordinary cohomology. We also construct the module structure of wrapped Floer cohomology over symplectic cohomology. These constructions yield new applications in symplectic topology relating to the Arnol'd chord conjecture and to exact contact embeddings. We prove that if a Liouville domain M admits an exact embedding into an exact convex symplectic manifold X, and the boundary of M…