Kevin Walker
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Registered User
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May 18 |
accepted | Do you recognise this variant of the cubes operad? |
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May 17 |
revised |
4D TQFT from a modular tensor category added 124 characters in body |
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May 16 |
comment |
4D TQFT from a modular tensor category [continued] ... a preferred boundary condition corresponding to gluing together many copies of (iterated) identity morphisms of the input $n$-category, and evaluation at this preferred boundary condition gives a preferred map from Hilbert spaces to the ground ring. If W is a 4-manifold with boundary, then applying this preferred map to the element $Z_{CYK}(W)$ of the Hilbert space gives an element of the ground ring which is equal to $Z_{WRT}(\partial(W))$. |
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May 16 |
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4D TQFT from a modular tensor category @David: I'm not sure I fully understand your question but I'll answer as best I can. I would say that $C$, or rather $Rep(C)$, is isomorphic to $Z_{CYK}(pt)$, not $Z_{CYK}(D^2)$. Perhaps part of the confusion is due to the fact that my TQFT framework is not the Atiyah-Segal framework. Compared to Atiyah-Segal, I have some extra structure at my disposal: "fields" or boundary conditions on manifolds. (The graph $\Gamma$ above is an example of such.) My Hilbert spaces are realized concretely as functions on boundary conditions. There is often... |
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May 16 |
answered | 4D TQFT from a modular tensor category |
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May 16 |
answered | Anomalies in the definition of Turaev’s TQFT |
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May 15 |
revised |
Picturing a Certain Torus and Klein Bottle fix TeX |
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May 15 |
answered | Picturing a Certain Torus and Klein Bottle |
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May 7 |
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Questions about knot (link) of surface in four dimension Should that be $H_1$ rather than $H_2$ in the second displayed equation? |
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Apr 22 |
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How unique are extensions of TQFTs to lower dimension? In answer to your first question: yes, right. I'm not sure about the second question (non-Morita-equivalent $(n-1)$-categories giving rise to same $(n-1, n)$ structure). I'm not even sure which way I would bet, if I had to bet. |
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Apr 22 |
answered | How unique are extensions of TQFTs to lower dimension? |
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Apr 14 |
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Quivers for algebras which are not basic or unital. @Dag: Yes, that does look like what I had in mind -- thanks! |
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Apr 13 |
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Quivers for algebras which are not basic or unital. My guess is that in the non-basic case one could start with the quiver for a Morita-equivalent basic algebra (as described above by B. Steinberg), then interpret each vertex $v_i$ as representing a $k_i \times k_i$ matrix algebra, each edge as representing a rectangular $k_i \times k_j$ matrix of elements of the radical, and so on. I don't know of a reference for this construction, and I would be very interested to know if there is one. |
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Mar 25 |
revised |
Conditions for a graph to be the 1- skeleton of a Surface added 157 characters in body |
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Mar 25 |
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Conditions for a graph to be the 1- skeleton of a Surface I understood the question as asking for a surface that was cap-off-able, but not capped off. But maybe I misunderstood. I'll edit the answer. |
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Mar 25 |
answered | Conditions for a graph to be the 1- skeleton of a Surface |
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Mar 2 |
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Multi-dimensional moment problem Thanks, I'll have a look at the references you mention. |
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Mar 2 |
revised |
Multi-dimensional moment problem fix typo |
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Feb 1 |
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The story about Milnor proving the Fáry-Milnor theorem Great video! I think I'll start using the same introductory soundtrack in my own lectures. |
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Jan 2 |
awarded | ● Good Answer |
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Dec 28 |
answered | slam-dunk operation |
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Dec 25 |
awarded | ● Nice Answer |
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Dec 25 |
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Morita equivalence for *-algebras I'm more interested in the linear (as opposed to conjugate-linear) case, since this is the case that corresponds to 1+1-dimensional unoriented TQFTs. But I'm also interested in the conjugate-linear case you mention, and of course you are right that one has to use the complex conjugate vector space $\overline M$ in that case. |
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Dec 24 |
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Morita equivalence for *-algebras Thanks for the suggestion. |
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Dec 24 |
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Morita equivalence for *-algebras Interesting idea -- thanks. |
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Dec 24 |
asked | Morita equivalence for *-algebras |
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Dec 10 |
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Algorithm to compute Heegard-Floer Homology? (continued) ...people who are a good for for MO; I'm fine with being unfriendly toward undergraduates looking for help with homework, etc.) |
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Dec 10 |
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Algorithm to compute Heegard-Floer Homology? Tim: Thanks for the response. I agree that ideally people should do the obvious Google searches before asking on MO. But I also think that keeping MO a friendly place is worthwhile, and voting to close (as opposed to gently reminding the new user that the answer is easy to find via google) strikes me as a little bit unfriendly. I think reasonable people can disagree about where to draw the line on too-obvious/too-googlable/etc, and for this reason one should give others the benefit of the doubt. (Just to clarify, I'm only advocating friendliness toward... |
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Dec 10 |
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Algorithm to compute Heegard-Floer Homology? It's not at all clear to me why this question should be closed. Many MO questions have brief answers of the form "See paper X". Do people think that all questions of this type should be closed? If not, what's different about this one? |
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Dec 10 |
answered | Algorithm to compute Heegard-Floer Homology? |
