Mathematical Field Notes

Archive for February 2015

A sanity check for the Fukaya category of a cotangent bundle

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Yesterday I gave a seminar about Fukaya categories and I didn’t have chance to do quite as much explicit computation as I’d hoped. I thought I’d write a blog post with a basic calculation to show you the kind of things that are involved in doing computations in Fukaya categories. I will show (using Abouzaid’s description of the zero section in terms of the cotangent fibre) that the zero section and the cotangent fibre have rank HF = 1, in the special case of T^*S^1. This is such a trivial result in the end (you could do the computation just by looking at the intersection and seeing it’s a single point) that you should think of this post as more of a sanity check.

The first 3 hours of what I said was essentially covering Auroux’s introduction to Fukaya categories (http://arxiv.org/abs/1301.7056), so if you look at that first, you should be able to figure out what I’m talking about. I hope that all my grading conventions agree with those of Abouzaid – if you notice a discrepancy, please let me know!

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Written by Jonny Evans

February 11, 2015 at 10:10 am

Posted in Uncategorized