Factorization homology and 4D TQFT

Alexander Kirillov; Ying Hong Tham

doi:10.4171/QT/159

Factorization homology and 4D TQFT

Alexander Kirillov
, Ying Hong Tham

Mathematics

Stony Brook University

Research output: Contribution to journal › Article › peer-review

7 Scopus citations

Abstract

In 2010, B. Balsam and A. Kirillov, Jr. showed that the Turaev–Viro invariants defined for a spherical fusion category A extends to invariants of 3-manifolds with corners. In 2021, A. Kirillov, Jr. described an equivalent formulation for the 2-1 part of the theory (2-manifolds with boundary) 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 by L. Crane and D. Yetter (1993).

Original language	English
Pages (from-to)	1-54
Number of pages	54
Journal	Quantum Topology
Volume	13
Issue number	1
DOIs	https://doi.org/10.4171/QT/159
State	Published - 2022

Keywords

Crane–Yetter
Extended topological field theory
factorization homology
TQFT

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abstract = "In 2010, B. Balsam and A. Kirillov, Jr. showed that the Turaev–Viro invariants defined for a spherical fusion category A extends to invariants of 3-manifolds with corners. In 2021, A. Kirillov, Jr. described an equivalent formulation for the 2-1 part of the theory (2-manifolds with boundary) 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 by L. Crane and D. Yetter (1993).",

keywords = "Crane–Yetter, Extended topological field theory, factorization homology, TQFT",

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AU - Tham, Ying Hong

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AB - In 2010, B. Balsam and A. Kirillov, Jr. showed that the Turaev–Viro invariants defined for a spherical fusion category A extends to invariants of 3-manifolds with corners. In 2021, A. Kirillov, Jr. described an equivalent formulation for the 2-1 part of the theory (2-manifolds with boundary) 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 by L. Crane and D. Yetter (1993).

KW - Crane–Yetter

KW - Extended topological field theory

KW - factorization homology

KW - TQFT

UR - https://www.scopus.com/pages/publications/85129039599

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JO - Quantum Topology

JF - Quantum Topology

IS - 1

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Factorization homology and 4D TQFT

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