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Symplectic Reduction Along A Submanifold, Peter Crooks, Maxence Mayrand
Symplectic Reduction Along A Submanifold, Peter Crooks, Maxence Mayrand
Mathematics and Statistics Faculty Publications
We introduce the process of symplectic reduction along a submanifold as a uniform approach to taking quotients in symplectic geometry. This construction holds in the categories of smooth manifolds, complex analytic spaces, and complex algebraic varieties, and has an interpretation in terms of derived stacks in shifted symplectic geometry. It also encompasses Marsden-Weinstein-Meyer reduction, Mikami-Weinstein reduction, the pre-images of Poisson transversals under moment maps, symplectic cutting, symplectic implosion, and the Ginzburg-Kazhdan construction of Moore-Tachikawa varieties in topological quantum field theory. A key feature of our construction is a concrete and systematic association of a Hamiltonian G-space 𝔐𝐺,𝑆 to …
Symplectic Groupoids And Generalized Almost Subtangent Manifolds, Fulya Şahi̇n
Symplectic Groupoids And Generalized Almost Subtangent Manifolds, Fulya Şahi̇n
Turkish Journal of Mathematics
We obtain equivalent assertions among the integrability conditions of generalized almost subtangent manifolds, the condition of compatibility of source and target maps of symplectic groupoids with symplectic form, and generalized subtangent maps.
Lie Groupoids And Generalized Almost Paracomplex Manifolds, Fulya Şahi̇n, Mustafa Habi̇l Gürsoy, İlhan İçen
Lie Groupoids And Generalized Almost Paracomplex Manifolds, Fulya Şahi̇n, Mustafa Habi̇l Gürsoy, İlhan İçen
Turkish Journal of Mathematics
In this paper, we show that there is a close relationship between generalized paracomplex manifolds and Lie groupoids. We obtain equivalent assertions among the integrability conditions of generalized almost paracomplex manifolds, the condition of compatibility of source and target maps of symplectic groupoids with symplectic form and generalized paraholomorphic maps.
From Double Lie Groupoids To Local Lie 2-Groupoids, Rajan Amit Mehta, Xiang Tang
From Double Lie Groupoids To Local Lie 2-Groupoids, Rajan Amit Mehta, Xiang Tang
Mathematics Sciences: Faculty Publications
We apply the bar construction to the nerve of a double Lie groupoid to obtain a local Lie 2-groupoid. As an application, we recover Haefliger's fundamental groupoid from the fundamental double groupoid of a Lie groupoid. In the case of a symplectic double groupoid, we study the induced closed 2-form on the associated local Lie 2-groupoid, which leads us to propose a definition of a symplectic 2-groupoid.