Open and Closed String field theory interpreted in classical Algebraic Topology

Heisenberg groups in algebraic topology

We study the Madsen-Tillmann spectrum $\C P^\infty_{-1}$ as a quotient of the Mahowald pro-object $\C P^{\infty}_{-\infty}$, which is closely related to the Tate cohomology of circle actions. That theory has an associated symplectic structure, whose symmetries define the Virasoro operations on the cohomology of moduli space constructed by Kontsevich and Witten.

来自无穷邻域的代数字符串拓扑

Algebraic string topology from the neighborhood of infinity

本文在配备pre-Calabi-Yau结构的光滑$A_\infty$-范畴的Hochschild链复形上构造了Goresky-Hingston环路余积的代数类似物，并利用范畴化形式穿孔无穷邻域和图形形式化给出显式模型，且在球面情形完成了显式计算。

TQFT - a new direction in algebraic topology

We give an introduction for the non-expert to TQFT (Topological Quantum Field Theory), focussing especially on its role in algebraic topology. We compare the Atiyah axioms for TQFT with the Eilenberg Steenrod axioms for homology, give a few simple examples of TQFTs, and discuss some other approaches that have been taken to defining TQFT. We then propose a new formulation of TQFT, which is closer in spirit to the way conventional functors of algebraic topology, like homology, are presented. In this approach the fundamental operation of gluing is incorporated through the notion of a *gluing morp…

Closed string operators in topology leading to Lie bialgebras and higher string algebra

This paper explains the conjectured algebraic duality between genus zero Gromov-Witten theory and genus zero "Closed String topology". This duality in another perspective is discussed on page 87 of the book "Frobenius manifold, quantum cohomology, and moduli spaces" (by Yuri Manin). This paper also discusses Fulton MacPherson strata.

三种风味下的弦拓扑

String topology in three flavours

本文从几何与代数两个视角研究Chas-Sullivan积和Goresky-Hingston余积，计算透镜空间上的运算并证明余积可区分三维透镜空间，同时用有理同伦论建立两种定义的等价性并讨论不变性。

泊松代数与转置泊松代数的运算新分裂及相关代数结构

New splittings of operations of Poisson algebras and transposed Poisson algebras and related algebraic structures

该研究针对泊松代数与转置泊松代数的双线性运算，提出经典分裂、第二种分裂与不分裂交错的混合分裂方式，通过代数表示刻画了两类代数各自对应的混合分裂结构，揭示了二者的差异。