# Mathematical Field Notes

## A sanity check for the Fukaya category of a cotangent bundle

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.