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.
-valued symmetric monoidal functors of the cobordism category and the objects of
Symmetric monoidal functors from the cobordism category correspond to topological quantum field theories.
The Eilenberg–Steenrod 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.