Scott Carter
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Registered User
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See also Professor Elvis Zap, or my home page which links to math art, my CV, and my talks page.
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1d |
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A family of words counted by the Catalan numbers Is there a way of traveling from one word to the next? That is can you label the vertices of the Stasheff polytope with these words in such a way that there is a well-defined method of getting from one to another? For example there is a cycle ()()()->(())()->(()()) ->((()))<-()(())<-()()(). When you represent these as $\cap$s you can think of the right foot of the cap sliding over the mountain to the right. In fact, I think if you combine this comment with Russ's you can get the correspondence. |
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May 18 |
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Braided Monoidal 2-categories with duals At this point, all these examples are too sophisticated for me in that I don't have the background knowledge to decipher the notation. Supposing that the examples work, then is there a scheme to color $2$-tangle diagrams and get non-trivial invariants of oriented knotted surfaces? |
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May 7 |
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Classification of higher dimensional manifolds I have not looked, but I suspect that Andrew Ranicki's book has a more modern approach. Still, I doubt that it will be readable for a novice. |
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Apr 26 |
answered | Visualize Fourth Homotopy Group of $S^2$ |
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Feb 20 |
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How to see the quaternionic hopf map generates the stable 3-stem? Not an answer, but some related material: Koschorke and Sanderson used the self-intersection (SI) maps of immersed 3-manifolds in 4-space to compute this group. Other results of Koschorke are relevant. Mike Freedman's paper on self-interestions of immersions also contains information. Peter Eccles wrote about the (SI) maps. Finally, the standard Froisart Morin sphere eversion can be shown to represent a generator. All of the results I mentioned are in published in the era (1978-1986). |
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Feb 15 |
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Second homotopy of a torus complement in the 4-sphere See also Sam Lomonaco's Pacific Math Journal paper. Here he is dealing with spheres, but the crossed module structure of $\pi_2$ should be interesting to you as well. |
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Feb 10 |
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Showing that a set elements of an octahedron symmetry group is a generating set Can you get ever signed permutation matrix this way? The question is more appropriate for math.stackexchange. |
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Feb 7 |
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What is the historical connection between Zeeman’s twist spinning and Fox’s Examples? I think I spoke to him about this. I will ask him again. |
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Jan 18 |
answered | 4D TQFT from a modular tensor category |
