Floer-like complexes for surfaces, maximally unlinked braids, and finite energy foliations

Floer-like complexes for surfaces, maximally unlinked braids, and finite energy foliations

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Barney Bramham, IAS
Fine Hall 801

In this talk I will present an approach to constructing finite energy foliations by pseudo-holomorphic curves with prescribed asymptotic orbits in the symplectization of a mapping torus. The idea is that so called maximally unlinked braids of periodic orbits support a Floer-like chain complex. The concept of unlinkedness comes from LeCalvez work on surface homeomorphisms, as I will explain. The upshot is that it allows us to essentially characterize finite energy foliations for mapping tori: also, these chain complexes should be of independent interest. I will draw a lot of pictures.