Some title containing the words "homotopy" and "symplectic", e.g. this one

Details Some title containing the words "homotopy" and "symplectic", e.g. this one Some title containing the words "homotopy" and "symplectic", e.g. this one

2001-05-10

arxiv.org/abs/math/0105080v3

Mathematics

Symplectic Geometry

based on a talk at "Poisson 2000", CIRM Marseille, June 2000; 19 pages, 4 figures, latex; v2: minor changes; v3: references to

Scientific paper

Using a basic idea of Sullivan's rational homotopy theory, one can see a Lie groupoid as the fundamental groupoid of its Lie algebroid. This paper studies analogues of Lie algebroids with non-trivial higher homotopy. Using various homotopy classes one can obtain e.g. central extensions of loop groups, or one can integrate a Lie biagebroid to a double symplectic groupoid. When combined with symplectic geometry, this idea leads to an infinite sequence of notions, starting with sympectic manifolds, Poisson manifolds and Courant algebroids. They are interrelated with higher-dimensional variational problems, and one can use them to define higher-dimensional Hamiltonian mechanics.

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