Structures and Diagrammatics of Four Dimensional Topological Lattice Field Theories

Two-block Springer fibers of types C and D: a diagrammatic approach to Springer theory

We explain an elementary topological construction of the Springer representation on the homology of (topological) Springer fibers of types C and D in the case of nilpotent endomorphisms with two Jordan blocks. The Weyl group and component group actions admit a diagrammatic description in terms of cup diagrams which appear in the definition of arc algebras of types B and D. We determine the decomposition of the representations into irreducibles and relate our construction to classical Springer theory. As an application we obtain presentations of the cohomology rings of all two-block Springer fi…

非经典纽结的代数与几何方面

Algebraic and Geometric Aspects of Non-Classical Knots

从比较几何和代数视角概述非经典纽结理论，探讨环境拓扑等变化如何导致具不同拓扑和组合特征的广义纽结理论，强调多种方法及不变量扩展，最后列出相关开放问题。

Invitation to Topological Conformal Field Theories

Topological conformal field theories are defined using only basic results from the theory of quasiconformal mappings.

拓扑场论中的同调代数与模空间

Homological algebra and moduli spaces in topological field theories

该研究为综述类工作，梳理了辛几何与规范理论领域的各类Floer理论及彼此关联。

Cyclic Foam Topological Field Theories

This paper proposes an axiomatic for Cyclic Foam Topological Field theories. That is Topological Field theories, corresponding to String theories, where particles are arbitrary graphs. World surfaces in this case are two-manifolds with one-dimensional singularities. We proved that Cyclic Foam Topological Field theories one-to-one correspond to graph-Cardy-Frobenius algebras, that are families $(A,B_\star,ϕ)$, where $A=\{A^s|s\in S\}$ are families of commutative associative Frobenius algebras, $B_\star = \bigoplus_{σ\inΣ} B_σ$ is an graduated by graphes, associative algebras of Frobenius type a…

Non-commutative extensions of two-dimensional topological field theories and Hurwitz numbers for real algebraic curves

It is well-known that classical two-dimensional topological field theories are in one-to-one correspondence with commutative Frobenius algebras. An important extension of classical two-dimensional topological field theories is provided by open-closed two-dimensional topological field theories. In this paper we extend open-closed two-dimensional topological field theories to nonorientable surfaces. We call them Klein topological field theories(KTFT). We prove that KTFTs bijectively correspond to algebras with certain additional structures, called structure algebras. Semisimple structure algebra…