Cobordism hypothesis

For a symmetric monoidal $(\backslash infty,\; n)$-category $\backslash mathcal\; \{C\}$ which is fully dualizable and every $k$-morphism of which is adjointable, for $1\backslash leq\; k\backslash leq\; n-1$, there is a bijection between the $\backslash mathcal\; \{C\}$-valued symmetric monoidal functors of the cobordism category and the objects of $\backslash mathcal\; \{C\}$.

Symmetric monoidal functors from the cobordism category correspond to topological quantum field theories. The cobordism hypothesis for topological quantum field theories is the analogue of the Eilenberg–Steenrod axioms for homology 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. In other words, the bijection between $\backslash mathcal\; \{C\}$-valued symmetric monoidal functors and the objects of $\backslash mathcal\; \{C\}$ is uniquely defined by its value for the point.

• Cobordism

{{reflist}}

• {{cite journal | last=Freed | first=Daniel S.|author-link=Dan Freed | title=The Cobordism hypothesis | journal=Bulletin of the American Mathematical Society | publisher=American Mathematical Society (AMS) | volume=50 | issue=1 | date=11 October 2012 | issn=0273-0979 | doi=10.1090/s0273-0979-2012-01393-9 | pages=57–92| doi-access=free }}
• [http://theoreticalatlas.wordpress.com/2013/04/22/seminar-on-cob-hyp/ Seminar on the Cobordism Hypothesis and (Infinity,n)-Categories], 2013-04-22
• Jacob Lurie (4 May 2009). On the Classification of Topological Field Theories

• {{nlab|id=cobordism+hypothesis|title=cobordism hypothesis}}

Category:Quantum field theory

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