Factorization homology and 4D TQFT

IF 1 2区数学 Q1 MATHEMATICS

Quantum Topology Pub Date : 2020-02-20 DOI:10.4171/QT/159

A. Kirillov, Ying Hong Tham

引用次数: 10

Abstract

In [BK], it is shown that the Turaev-Viro invariants defined for a spherical fusion category $\mathcal{A}$ extends to invariants of 3-manifolds with corners. In [Kir], an equivalent formulation for the 2-1 part of the theory (2-manifolds with boundary) is described using the space of "stringnets with boundary conditions" as the vector spaces associated to 2-manifolds with boundary. Here we construct a similar theory for the 3-2 part of the 4-3-2 theory in [CY1993].

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分解同调与4D TQFT

在[BK]中，证明了为球面融合范畴$\mathcal{a}$定义的Turaev-Viro不变量可推广到带角的3流形的不变量。在[Kir]中，使用“带边界条件的弦网”空间作为与带边界的2-流形相关的向量空间，描述了理论2-1部分(带边界的2-流形)的等效公式。在这里，我们对[CY1993]中4-3-2理论的3-2部分构建了一个类似的理论。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Quantum Topology Mathematics-Geometry and Topology

CiteScore

1.80

自引率

9.10%

发文量

期刊介绍： Quantum Topology is a peer reviewed journal dedicated to publishing original research articles, short communications, and surveys in quantum topology and related areas of mathematics. Topics covered include in particular: Low-dimensional Topology Knot Theory Jones Polynomial and Khovanov Homology Topological Quantum Field Theory Quantum Groups and Hopf Algebras Mapping Class Groups and Teichmüller space Categorification Braid Groups and Braided Categories Fusion Categories Subfactors and Planar Algebras Contact and Symplectic Topology Topological Methods in Physics.