Twin TQFTs and Frobenius algebras

TQFT的符号与双桥结的迹域

Signatures of TQFTs and trace fields of two-bridge knots

本文证明了支配SO$_3$ TQFT符号的Frobenius代数包含双桥结的迹域，揭示了低维拓扑中两个先验无关对象间的有趣关系。

Defining and classifying TQFTs via surgery

We give a presentation of the $n$-dimensional oriented cobordism category $\text{Cob}_n$ with generators corresponding to diffeomorphisms and surgeries along framed spheres, and a complete set of relations. Hence, given a functor $F$ from the category of smooth oriented manifolds and diffeomorphisms to an arbitrary category $C$, and morphisms induced by surgeries along framed spheres, we obtain a necessary and sufficient set of relations these have to satisfy to extend to a functor from $\text{Cob}_n$ to $C$. If $C$ is symmetric and monoidal, then we also characterize when the extension is a T…

关于可定向二维带状体的TQFT注记

A note on TQFTs for orientable 2-dimensional cobordisms

本文提出一个中间框架，用于分类可定向二维带状体的TQFT，以解决非定向情况下分类所需的额外数据问题。

Algebraic Structures Derived from Foams

Foams are surfaces with branch lines at which three sheets merge. They have been used in the categorification of sl(3) quantum knot invariants and also in physics. The 2D-TQFT of surfaces, on the other hand, is classified by means of commutative Frobenius algebras, where saddle points correspond to multiplication and comultiplication. In this paper, we explore algebraic operations that branch lines derive under TQFT. In particular, we investigate Lie bracket and bialgebra structures. Relations to the original Frobenius algebra structures are discussed both algebraically and diagrammatically.

近 Frobenius 代数中（余）单位的必要性

The necessity of (co)unit in nearly Frobenius algebra

本文研究近 Frobenius 代数中（余）单位的必要性，证明主理想整环上乘法满射且余乘法单射的近 Frobenius 代数必为 Frobenius 代数，并服务于链环同调构造探索。

整性与Hennings TQFTs的规范依赖性

Integrality and Gauge Dependence of Hennings TQFTs

本文基于有限Hopf代数构造整性TQFTs，展示其在Hennings不变量中的应用，并通过规范变换建立TQFT函子的同构，证明量子sl_2的不变量取值于循环整数。