Submanifolds in Poisson geometry

2021 ◽  
pp. 157-191
Keyword(s):  

These volumes contain the proceedings of the conference held at Aarhus, Oxford and Madrid in September 2016 to mark the seventieth birthday of Nigel Hitchin, one of the world’s foremost geometers and Savilian Professor of Geometry at Oxford. The proceedings contain twenty-nine articles, including three by Fields medallists (Donaldson, Mori and Yau). The articles cover a wide range of topics in geometry and mathematical physics, including the following: Riemannian geometry, geometric analysis, special holonomy, integrable systems, dynamical systems, generalized complex structures, symplectic and Poisson geometry, low-dimensional topology, algebraic geometry, moduli spaces, Higgs bundles, geometric Langlands programme, mirror symmetry and string theory. These volumes will be of interest to researchers and graduate students both in geometry and mathematical physics.


Author(s):  
Shahn Majid ◽  
◽  
Liam Williams ◽  

We semiclassicalise the theory of quantum group principal bundles to the level of Poisson geometry. The total space X is a Poisson manifold with Poisson-compatible contravariant connection, the fibre is a Poisson-Lie group in the sense of Drinfeld with bicovariant Poisson-compatible contravariant connection, and the base has an inherited Poisson structure and Poisson-compatible contravariant connection. The latter are known to be the semiclassical data for a quantum differential calculus. The theory is illustrated by the Poisson level of the q-Hopf fibration on the standard q-sphere. We also construct the Poisson level of the spin connection on a principal bundle.


2020 ◽  
Vol 2020 (2) ◽  
Author(s):  
Thomas Basile ◽  
Euihun Joung ◽  
Jeong-Hyuck Park
Keyword(s):  

2013 ◽  
Vol 8-9 ◽  
pp. 405-412
Author(s):  
Gîrban Anania Anania Aron ◽  
Gabriel Girban

Through this paper is presented a geometric approach of a battery electrochemical model using specific tools from the Poisson geometry.


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