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

By P. Ševera. 2001

233 citations recorded by the source corpus.

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.

Subfields: Algebra and Number Theory, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/3273ba4fbb4515bf1d67bcf65a4c72f5c9236aa0

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In Algebra and Number Theory

In Mathematical Physics

Citations in the corpus

Coisotropic submanifolds in Poisson geometry and branes in the Poisson sigma model (2003, unknown): “4 Using the language of Lie algebroids, one may also give the following interpretation [19, 9]: Elements of C(M) are precisely those bundle maps that are also morphisms of Lie algebroids, where the tangent bundles are given the canonical Lie algebroid structure and T ∗M the one induced from the Pois”
Graded bundles and homogeneity structures (2011, methodology): “This notion is equivalent to the notion of an N-manifold in the terminology of Ševera and Roytenberg [11, 9].”
Q-algebroids and their cohomology (2007, background): “e the [k] on the right-hand side is the usual degreeshift functor for graded vector spaces. This is our main justiﬁcation for why our notation for the degree-shift functor diﬀers by a sign from, e.g. [13, 33, 35]. It is clear that, at least locally, a degree jsection Xis completely determined by the”
Supergroupoids, double structures, and equivariant cohomology (2006, methodology): “[33], [63], [68], where the notation E[−j] has been used for the supermanifold which we denote by [j]E.”
On the structure of graded symplectic supermanifolds and Courant algebroids (2002, methodology): “A s an application ofthese ideas,we prove the acyclicity of \higherde R ham com plexes",a generalization ofa classicresultofFr ohlicherN ijenhuis,and derive severaleasy but usefulcorollaries.”
Integrating $L_\infty $-algebras (2006, methodology): “For this purpose, we use the Yoneda functor y : C → {Sheaves on C} X → (T → hom(T,X))”