Results 41 to 50 of about 212,635 (101)

Remarks on Symplectic Geometry [PDF]

arXiv, 2019
We survey the progresses on the study of symplectic geometry past four decades. We briefly deal with the convexity properties of a moment map, the classification of symplectic actions, the symplectic embedding problems, and the theory of Gromov-Witten invariants.
arxiv  

Connections under Symplectic Reduction [PDF]

arXiv, 2000
In this note we give conditions which ensure the reduction of a symplectic connection in the process of a Marsden-Weinstein reduction and of the reduction of a presymplectic manifold.
arxiv  

Marsden-Weinstein reduction for symplectic connections [PDF]

arXiv, 2001
We propose a reduction procedure for symplectic connections with symmetry. This is applied to coadjoint orbits whose isotropy is reductive.
arxiv  

Higher Order Geometric Theory of Information and Heat Based on Poly-Symplectic Geometry of Souriau Lie Groups Thermodynamics and Their Contextures: The Bedrock for Lie Group Machine Learning

Entropy, 2018
We introduce poly-symplectic extension of Souriau Lie groups thermodynamics based on higher-order model of statistical physics introduced by Ingarden. This extended model could be used for small data analytics and machine learning on Lie groups.
F. Barbaresco
semanticscholar   +1 more source

On a generalization of a theorem of McDuff [PDF]

arXiv, 2011
We study the symplectic structure of the holomorphic coadjoint orbits, generalizing a theorem of McDuff on the symplectic structure of Hermitian symmetric spaces of noncompact type.
arxiv  

Monodromy invariants in symplectic topology

, 2003
This text is a set of lecture notes for a series of four talks given at I.P.A.M., Los Angeles, on March 18-20, 2003. The first lecture provides a quick overview of symplectic topology and its main tools: symplectic manifolds, almost-complex structures ...
Auroux, Denis
core   +2 more sources

Reeb-Thurston stability for symplectic foliations [PDF]

arXiv, 2013
We prove a version the local Reeb-Thurston stability theorem for symplectic foliations.
arxiv  

Stability conditions in symplectic topology [PDF]

arXiv, 2017
We discuss potential (largely speculative) applications of Bridgeland's theory of stability conditions to symplectic mapping class groups.
arxiv  

Erratum: On the monodromy of irreducible symplectic manifolds \n (Algebraic Geometry 3 (2016), no. 3, 385–391)

Algebraic Geometry, 2023
Giovanni Mongardi
semanticscholar   +1 more source

Fukaya categories and deformations

, 2002
This is an informal (and mostly conjectural) discussion of some aspects of Fukaya categories. We start by looking at exact symplectic manifolds which are obtained from a closed Calabi-Yau by removing a hyperplane section.
Seidel, Paul
core   +2 more sources