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Topological quantum field theory.

9 votes
0 answers
407 views

Why does the index of the Dirac operator on a manifold with boundary live inside the Pfaffia...

I am trying to understand a statement from page 72 of What is an elliptic object? by Stolz and Teichner. They have a spin Riemannian 2-manifold $\Sigma$, with boundary 1-manifold $Y$. The Dirac oper …
Sam Gunningham's user avatar
6 votes
0 answers
510 views

Is there a version of the 2d cobordism hypothesis for surfaces with non-empty incoming and o...

Question: Is there a condition on an object $x$ of an $(\infty,2)$-category $\mathcal C$ which is equivalent to $x = Z(pt_+)$ for a unique TFT $Z$ from the $(\infty,2)$-category of framed bordisms whe …
Sam Gunningham's user avatar
15 votes
2 answers
935 views

Homotopy Fixed Points of SO(2) on Fully Dualizable Algebras

Note: by fixed points, I always mean homotopy fixed points. As explained in Jacob Lurie's paper on the cobordism hypothesis, we have an action of O(2) on the $\infty $-groupoid $X$ given by consideri …
Sam Gunningham's user avatar