
TL;DR
This paper provides a detailed introduction to Tamarkin category theory from a quantitative perspective, illustrating its applications in symplectic topology and its relation to persistent homology, with numerous examples for geometric intuition.
Contribution
It offers a comprehensive exposition of Tamarkin category theory, connecting it to symplectic techniques and generalizing persistent homology, with practical applications and illustrative examples.
Findings
Tamarkin category effectively encodes symplectic invariants.
Sheaf-theoretic methods unify various symplectic techniques.
Generalizations of persistent homology are naturally incorporated.
Abstract
This is a lecture note from a seminar course given at Tel Aviv University in Spring 2018. Part of the preliminary section is built from Kazhdan's seminar organized in the Hebrew University of Jerusalem in Fall 2017. The main topic of this note is a detailed introduction of Tamarkin category theory from a quantitative perspective, followed by a demonstration of various applications in symplectic topology. Many examples are provided in order to obtain certain geometric intuitions of those abstract algebraic constructions in Tamarkin category. In this note, 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…
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Topological and Geometric Data Analysis · Algebraic structures and combinatorial models
