nLab On the Classification of Topological Field Theories

This entry is about the article

• Jacob Lurie:

  On the Classification of Topological Field Theories

  Current Developments in Mathematics Volume 2008 (2009), 129-280

  arXiv:0905.0465

  doi:10.4310/CDM.2008.v2008.n1.a3

  euclid:cdm/1254748657

whose main content is a formalization and proof of the

• cobordism hypothesis.

Contents

1. Topological Field Theories and Higher Categories

• higher category theory

• (infinity,n)-category

• quantum field theory

  • FQFT

• n-categorical physics

2. Formulation of the Cobordism Hypothesis

• complete Segal space

• cobordism

• (infinity,n)-category of cobordisms

• cobordism hypothesis

  • generalized tangle hypothesis

3. Proof of the Cobordism Hypothesis

4. Beyond the Cobordism Hypothesis

• factorization algebra

• Calabi-Yau object

• TCFT

category: reference