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Introduction

  • Jun Zhang
Chapter
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Part of the CRM Short Courses book series (CRMSC)

Abstract

This chapter gives a brief overview of the primary materials in this book. It starts from the background of symplectic geometry with two famous results: Gromov’s non-squeezing theorem and Arnold’s conjecture (Lagrangian version). Then a discussion on the key concept of singular support follows, with an emphasis on its geometric interpretation. With the concept of singular support, Tamarkin categories will be described, and the Guillermou-Kashiwara-Schapira sheaf quantization will be formulated. These form the underlying platform where various symplectic objects can be expressed in terms of sheaves. Moreover, there is a section devoted to the background material on persistence k-modules, which can be viewed as elements in a special Tamarkin category; there is another section introducing Hofer’s geometry, which is an iconic quantitative apparatus in symplectic geometry. Finally, a brief argument showing that the sheaf counterpart of the standard symplectic homology can be constructed from a certain projector in a Tamarkin category will be provided. This yield an alternative approach to study domains of Euclidean spaces.

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Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Jun Zhang
    • 1
  1. 1.Département de Mathématiques et StatistiqueUniversity of MontrealMontréalCanada

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