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for homology theories. The
EilenbergâSteenrod axioms state that a homology theory is uniquely determined by its value for the point, so analogously what the cobordism hypothesis states is that a topological quantum field theory is uniquely determined by its value for the point. In other words, the
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outlined a proof of the cobordism hypothesis, though the details of his approach have yet to appear in the literature as of 2022. In 2021, Daniel Grady and Dmitri Pavlov claimed a complete proof of the cobordism hypothesis, as well as a generalization to
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Baez, John C.; Dolan, James (1995). "Higherâdimensional algebra and topological quantum field theory".
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Grady, Daniel; Pavlov, Dmitri (2021-11-01). "The geometric cobordism hypothesis".
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Mathematical
Foundations of Quantum Field Theory and Perturbative String Theory
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Ayala, David; Francis, John (2017-05-05). "The cobordism hypothesis".
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Symmetric monoidal functors from the cobordism category correspond to
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Seminar on the
Cobordism Hypothesis and (Infinity,n)-Categories
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and James Dolan, concerns the classification of extended
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Classification of topological quantum field theories
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162:{\displaystyle 1\leq k\leq n-1}
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