Given a compact symplectic manifold whose symplectic form has integer periods, one associates to it a dg category based on the microlocal analysis according to Kashiwara-Schapira.
…we try to explain how standard symplectic techniques, for instance, generating function, capacities, symplectic homology, etc., are elegantly packaged in the language of sheaves as well as related intriguing sheaf operators. In addition, many concepts developed in Tamarkin category theory are natural generalizations of persistent homology theory…
Vivek Shende, Microlocal category for Weinstein manifolds via h-principle, arXiv:1707.07663
Sheng-Fu Chiu, Non-squeezing property of contact balls, doi arXiv:1405.1178
In this paper we solve a contact non-squeezing conjecture proposed by Eliashberg, Kim and Polterovich. Let BR be the open ball of radius $R$ in $\mathbb{R}^{2n}$ and let $\mathbb{R}^{2n}\times S^1$ be the prequantization space equipped with the standard contact structure. Following Tamarkin’s idea, we apply microlocal category methods to prove that if $R$ and $r$ satisfy $1\leq \pi r^2 \lt \pi R^2$, then it is impossible to squeeze the contact ball $B_R\times S^1$ into $B_r\times S^1$ via compactly supported contact isotopies.
Created on September 20, 2022 at 22:33:27. See the history of this page for a list of all contributions to it.