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Deformations of pre-symplectic structures and the Koszul L-infty-algebra Schätz, Florian ; E-print/Working paper (2017) We study the deformation theory of pre-symplectic structures, i.e. closed two-forms of fixed rank. The main result is a parametrization of nearby deformations of a given pre-symplectic structure in terms ... [more ▼] We study the deformation theory of pre-symplectic structures, i.e. closed two-forms of fixed rank. The main result is a parametrization of nearby deformations of a given pre-symplectic structure in terms of an $L_\infty$-algebra, which we call the Koszul $L_\infty$-algebra. This $L_\infty$-algebra is a cousin of the Koszul dg Lie algebra associated to a Poisson manifold, and its proper geometric understanding relies on Dirac geometry. In addition, we show that a quotient of the Koszul $L_{\infty}$-algebra is isomorphic to the $L_\infty$-algebra which controls the deformations of the underlying characteristic foliation. Finally, we show that the infinitesimal deformations of pre-symplectic structures and of foliations are both obstructed. [less ▲] Detailed reference viewed: 59 (0 UL)Equivalences of coisotropic submanifolds Schatz, Florian ; in Journal of Symplectic Geometry (2017), 15(1), 107-149 We study the role that Hamiltonian and symplectic diffeomorphisms play in the deformation problem of coisotropic submanifolds. We prove that the action by Hamiltonian diffeomorphisms corresponds to the ... [more ▼] We study the role that Hamiltonian and symplectic diffeomorphisms play in the deformation problem of coisotropic submanifolds. We prove that the action by Hamiltonian diffeomorphisms corresponds to the gauge-action of the L-infinity-algebra of Oh and Park. Moreover we introduce the notion of extended gauge-equivalence and show that in the case of Oh and Park's L-infinity-algebra one recovers the action of symplectic isotopies on coisotropic submanifolds. Finally, we consider the transversally integrable case in detail. [less ▲] Detailed reference viewed: 88 (2 UL)Deformations of coisotropic submanifolds for fibrewise entire Poisson structures Schatz, Florian ; in Letters in Mathematical Physics (2013), 103(7), 777-791 We show that deformations of a coisotropic submanifold inside a fibrewise entire Poisson manifold are controlled by the L-infinity-algebra introduced by Oh-Park (for symplectic manifolds) and Cattaneo ... [more ▼] We show that deformations of a coisotropic submanifold inside a fibrewise entire Poisson manifold are controlled by the L-infinity-algebra introduced by Oh-Park (for symplectic manifolds) and Cattaneo-Felder. In the symplectic case, we recover results previously obtained by Oh-Park. Moreover we consider the extended deformation problem and prove its obstructedness. [less ▲] Detailed reference viewed: 78 (1 UL) |
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