Fundamentals for Symplectic $\mathcal{A}$-modules
Anastasios Mallios, Patrice P. Ntumba
TL;DR
This paper explores how sheaf-theoretic Abstract Differential Geometry can be applied to classical symplectic geometry, aiming to unify and extend traditional geometric concepts.
Contribution
It introduces a sheaf-theoretic framework for symplectic geometry within Abstract Differential Geometry, providing a new perspective and potential generalizations.
Findings
Sheaf-theoretic approach unifies classical symplectic concepts.
Potential for extending symplectic geometry using Abstract Differential Geometry.
Lays groundwork for further exploration of implications in future work.
Abstract
Sheaf theoretically based Abstract Differential Geometry incorporates and generalizes all the classical differential geometry. Here, we undertake to partially explore the implications of Abstract Differential Geometry to classical symplectic geometry. The full investigation will be presented elsewhere.
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Taxonomy
TopicsGeometric and Algebraic Topology · Homotopy and Cohomology in Algebraic Topology · Algebraic Geometry and Number Theory