Mirror symmetry and actions of braid groups on derived categories
R. P. Thomas
TL;DR
This paper surveys joint work on mirror symmetry, braid group actions, and derived categories, highlighting the interplay between algebraic and symplectic geometry in the context of mirror symmetry.
Contribution
It introduces new insights into how braid groups act on derived categories, advancing understanding of mirror symmetry and categorical symmetries.
Findings
Braid group actions on derived categories are linked to mirror symmetry.
New categorical frameworks for mirror symmetry are proposed.
Connections between algebraic and symplectic geometry are elucidated.
Abstract
Talk given at Harvard, January 1999, published in the Proceedings of the Harvard Winter School on mirror symmetry, vector bundles and lagrangian cycles, 1999, International Press. Surveys the joint work [ST, KS] with Paul Seidel and Mikhail Khovanov.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models · Advanced Algebra and Geometry