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Higher Symplectic Geometry

open access: yes, 2011
We consider generalizations of symplectic manifolds called n-plectic manifolds. A manifold is n-plectic if it is equipped with a closed, nondegenerate form of degree n+1. We show that higher structures arise on these manifolds which can be understood as the categorified or homotopy analogues of important structures studied in symplectic geometry and ...
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On the hyperbolic symplectic geometry

open access: yesJournal of Combinatorial Theory, Series A, 2004
The present article provides a new characterization of the geometry on the points and hyperbolic lines of a non-degenerate symplectic polar space. This characterization is accomplished by studying the family of subspaces obtained when considering the polars of all hyperbolic lines. Let \(\mathbb W_{2n-1}(\mathbb F)\) denote the polar space with respect
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Symplectic geometry of conical symplectic resolutions

open access: yes, 2021
Ever since Kronheimer's celebrated hyperkähler construction of gravitational instantons thirty years ago, many similar constructions have appeared in the mathematical literature, eventually producing a vast class of holomorphic symplectic manifolds nowadays called Conical Symplectic Resolutions (CSRs).
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