Event
Maia Fraser, Universit茅 d'Ottawa
Contact non-squeezing - a low-tech proof in the language of persistence modules.
聽Viterbo's symplectic capacity of domains in $R^{2n}$ and Sandon's contact capacity of domains in $R^{2n} imes S^1$ are persistences of certain homology classes in the persistence modules formed by generating function (GF) homology groups. These GF-based capacities provide alternate proofs of non-squeezing in their respective settings, results originally due to Gromov and Eliashberg-Kim-Polterovich (EKP) respectively. While Gromov proved the ball $B(R)$ cannot be squeezed into a narrower cylinder, the contact analog that EKP considered in $R^{2n} imes S^1$, namely squeezing of a pre-quantized ball $B(R) imes S^1$ into itself, was ruled out by EKP only for integer R while they showed squeezing actually holds for R<1. Non-squeezing via a contact isotopy for all R>1 was established by Chiu (2014) using sheaf theory. I will describe a low-tech proof of this result using analogs of Viterbo-Sandon capacities. I first introduce filtration-decreasing morphisms between GF homology groups that set up a functor from a sub-category of $calD imes Z$ to Vect, where $calD$ is the category of bounded domains with inclusion. Persistences in this persistence module then yield a sequence of integer-valued contact invariants for pre-quantized balls which rule out squeezing.聽