Classification of topological quantum field theories
In mathematics, the cobordism hypothesis, due to John C. Baez and James Dolan,[1] concerns the classification of extended topological quantum field theories (TQFTs). In 2008, Jacob Lurie outlined a proof of the cobordism hypothesis, though the details of his approach have yet to appear in the literature as of 2022.[2][3][4] In 2021, Daniel Grady and Dmitri Pavlov claimed a complete proof of the cobordism hypothesis, as well as a generalization to bordisms with arbitrary geometric structures.[4]
^Baez, John C.; Dolan, James (1995). "Higher‐dimensional algebra and topological quantum field theory". Journal of Mathematical Physics. 36 (11): 6073–6105. arXiv:q-alg/9503002. Bibcode:1995JMP....36.6073B. doi:10.1063/1.531236. ISSN 0022-2488. S2CID 14908618.
^Hisham Sati; Urs Schreiber (2011). Mathematical Foundations of Quantum Field Theory and Perturbative String Theory. American Mathematical Soc. p. 18. ISBN 978-0-8218-5195-1.
^Ayala, David; Francis, John (2017-05-05). "The cobordism hypothesis". arXiv:1705.02240 [math.AT].
^ abGrady, Daniel; Pavlov, Dmitri (2021-11-01). "The geometric cobordism hypothesis". arXiv:2111.01095 [math.AT].
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