Symplectic Geometry
Symplectic manifolds, moment maps, and Floer theory.
Symplectic Geometry. Symplectic manifolds, moment maps, and Floer theory.
Foundations and canonical references
The standard treatments of symplectic geometry approach the subject from complementary angles. Mcduff, Introduction to Symplectic Topology (2017) is the anchor reference for the subject and lays out the core definitions, theorems, and worked examples that practitioners return to. Cannas, Lectures on Symplectic Geometry (2008) gives a parallel, more proof-oriented exposition of the same material and is widely used as a graduate text.
Open methodological questions for symplectic geometry include sharpening the bridges between foundational theory and computational practice, extending classical results to broader or more structured settings, and integrating the techniques surveyed above with adjacent mathematical disciplines. The references listed in this page are the entry points that current work builds on.
Prerequisites
Sources
- textbook · primary · 2017Introduction to Symplectic Topologymcduff-2017, salamon-2017
- textbook · primary · 2008Lectures on Symplectic Geometrycannas-2008
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