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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Notes
- 1.
This is based on a discussion and joint work with Leonid Polterovich.
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Zhang, J. (2020). Introduction. In: Quantitative Tamarkin Theory. CRM Short Courses. Springer, Cham. https://doi.org/10.1007/978-3-030-37888-2_1
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