On the Classification of Topological Field Theories
By Jacob Lurie. 2009
631 citations recorded by the source corpus.
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.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/5817e854cc4f420574a4d923cec4f0cee173f228
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In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- Symplectic cohomology and Viterbo's theorem (2013, background): “Lurie has sketched an argument in [55] that the resulting BV∞ structure is also dependent only on the homotopy type.”
- The higher Morita category of n–algebras (2014, background): “In this more general setting, Lurie was able to prove the Cobordism Hypothesis (although so far only a detailed sketch [31] of the proof has appeared).”
- Wall-crossing in coupled 2d-4d systems (2011, background): “Finally, in topological field theory, a whole hierarchy of defects leads to a beautiful mathematical structure involving higher category theory [9, 10, 11, 12, 13, 14].”
- Anomalies in the space of coupling constants and their dynamical applications II (2019, background): “This point of view is highly developed for topological field theories, as for example in [77–79].”
- Gauging spatial symmetries and the classification of topological crystalline phases (2016, methodology): “For theories admitting gapped (therefore topological in the IR) boundary conditions, this is the Baez-Dolan-Lurie cobordism theorem (sometimes “hypothesis”) [72, 78], which characterizes possible boundary data as special objects in a d + 1category C.”