Peng Zhou

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blog:2022-12-18 [2022/12/18 16:36] pzhoublog:2022-12-18 [2023/06/25 15:53] (current) – external edit 127.0.0.1
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 (hmm, what is a 4d TFT? Is the category of abelian group a monoidal category? Yes, there is tensor product defined. So, to the empty 2-manifold, we should assign the coefficient category, Ab. And to a closed 3-manifold $Y$, we should assign a functor from Ab to Ab, which I think should be the monoidal unit, $1$. In the cat of Ab, it is $\Z$. See also [[https://authors.library.caltech.edu/66625/2/icm2010.3.2021.2043.pdf | Kapustin's 2010 ICM talk notes]] (hmm, what is a 4d TFT? Is the category of abelian group a monoidal category? Yes, there is tensor product defined. So, to the empty 2-manifold, we should assign the coefficient category, Ab. And to a closed 3-manifold $Y$, we should assign a functor from Ab to Ab, which I think should be the monoidal unit, $1$. In the cat of Ab, it is $\Z$. See also [[https://authors.library.caltech.edu/66625/2/icm2010.3.2021.2043.pdf | Kapustin's 2010 ICM talk notes]]
  
-What is Heegaard-Floer theory? Do we just do the usual Floer homology of two torus in a symmetric product of surfaces? OK. That's sort of easy. But, how to think about symmetric product of Lagrangians? Aha, and Ozsvath-Szabo has that solved already, [[https://arxiv.org/pdf/math/0309170.pdf | for branched double cover.]] +What is Heegaard-Floer theory? Do we just do the usual Floer homology of two torus in a symmetric product of surfaces? OK. That's sort of easy. But, how to think about symmetric product of Lagrangians? 
  
 +What is a k-handle? It is basically some fat version of $k$-manifold in a ambient space. 
  
  
  
 +===== Ozsvath-Szabo paper =====
 +https://arxiv.org/pdf/math/0101206.pdf
 +
 +Why there are so many versions of Heegaard-Floer theory? And why there is the funny dependence on spin-c? (what is spin-c?
 +
 +Oh, I see now. 
  
  
  
blog/2022-12-18.1671381376.txt.gz · Last modified: 2023/06/25 15:53 (external edit)