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- Talks will be 50 minutes + 10 minutes of questions, but feel free to stay afterwards to chat if you'd like.
- The first 60 minutes of our meetings will be recorded so that those who can't make it to the live meeting can still watch the talks. We plan on making these videos available online.
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Abstract: Khovanov categorified the Jones polynomial by constructing a corresponding link homology. His construction admits an anticommutative version (referred to as 'odd') that was developed by Ozsváth, Rasmussen and Szabó. The usual (or 'even') construction extends to tangles, taking the form of the homotopy type of a complex of bimodules over the arc algebra. The 'odd' equivalent to the arc algebra is non-associative, making it not clear what a bimodule over it should be. In the first part of the talk, I'll explain how ORS construction works in the context of chronological cobordisms, as introduced by Putyra. Then, I'll sketch how to extend this to tangles by using an odd version of arc algebras. We will quickly see that it is not naively possible to use it to construct an odd invariant, mainly because the odd arc algebra is not associative. In the second part of the talk, I'll explain how, by changing the monoidal category of vector spaces we work in, we can solve the non-associativity issue of the arc algebra. Then, we will sketch how to use it to construct an odd version of Khovanov invariant for tangles. This is a joint work with Krzysztof Putyra.
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