nLab microlocal category

• Dmitry Tamarkin, Microlocal category for a closed symplectic manifold, talk at IAS youtube
• Boris Tsygan, A microlocal category associated to a symplectic manifold, talk youtube
• Dmitry Tamarkin, Microlocal category, arXiv:1511.08961

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.

• Boris Tsygan, A microlocal category associated to a symplectic manifold, In: M. Hitrik, D. Tamarkin, B. Tsygan, S. Zelditch (eds), Algebraic and Analytic Microlocal Analysis. AAMA 2013. Springer Proc. in Math. & Stat. 269 doi
• Jun Zhang, Quantitative Tamarkin theory, book, CRM Short Courses, arXiv:1807.09878

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…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.

category: geometry, analysis