On the Classification of Topological Field Theories

2009/05/04 by Jacob Lurie, Lurie, Jacob · 1 voice · 91 citations
Computer Science · Mathematics · #55N22 #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #Category Theory (math.CT) #Combinatorics #FOS: Mathematics #Field (mathematics) #Homotopy and Cohomology in Algebraic Topology #Mathematics #Physics #Pure mathematics #Theoretical physics #Topological and Geometric Data Analysis #Topology (electrical circuits) #math.AT #math.CT #msc:55N22

paper · pdf · doi:10.48550/arxiv.0905.0465

published in arXiv (Cornell University) (Cornell University) · 111 pages

arxiv created 2009/05/04 · openalex publication_date 2009/05/04 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

This paper provides an informal sketch of a proof of the Baez-Dolan cobordism hypothesis, which provides a classification for extended topological quantum field theories.

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Discussions

• The standard argument is that the Abelian nature of $p$ -form symmetries ( $p\ge1$ ) follows from their definition as topological operators $U(M^{d-p-1})$ acting on a spatial slice $\Sigma$ . For homo [stackexchange, 1 points]

Related

• On the Classification of Topological Field Theories
• The cobordism hypothesis
• A higher category of cobordisms and topological quantum field theory
• The Classification of Two Dimensional topological Field Theories
• Topological quantum field theories