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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 …
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 …
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 …