Between generalized complex and Poisson geometry

Abstract Generalized contact bundles are odd-dimensional analogues of generalized complex manifolds. They have been introduced recently and very little is known about them. In this paper we study their local structure. Specifically, we prove a local splitting theorem similar to those appearing in Poisson geometry. In particular, in a neighborhood of a regular point, a generalized contact bundle is either the product of a contact and a complex manifold or the product of a symplectic manifold and a manifold equipped with an integrable complex structure on the gauge algebroid of the trivial line bundle.

Download Full-text

Simultaneous deformations and Poisson geometry

Compositio Mathematica ◽

10.1112/s0010437x15007277 ◽

2015 ◽

Vol 151 (9) ◽

pp. 1763-1790 ◽

Cited By ~ 10

Author(s):

Yaël Frégier ◽

Marco Zambon

Keyword(s):

Complex Geometry ◽

Poisson Manifolds ◽

Poisson Geometry ◽

Complex Structures ◽

Poisson Structures ◽

Coisotropic Submanifolds ◽

Generalized Complex ◽

Derived Bracket

We consider the problem of deforming simultaneously a pair of given structures. We show that such deformations are governed by an $L_{\infty }$-algebra, which we construct explicitly. Our machinery is based on Voronov’s derived bracket construction. In this paper we consider only geometric applications, including deformations of coisotropic submanifolds in Poisson manifolds, of twisted Poisson structures, and of complex structures within generalized complex geometry. These applications cannot be, to our knowledge, obtained by other methods such as operad theory.

Download Full-text

Geometry and Physics: Volume II

10.1093/oso/9780198802020.001.0001 ◽

2018 ◽

Keyword(s):

Moduli Spaces ◽

Mirror Symmetry ◽

Geometric Analysis ◽

Mathematical Physics ◽

Poisson Geometry ◽

Special Holonomy ◽

Low Dimensional Topology ◽

Generalized Complex Structures ◽

Wide Range ◽

Low Dimensional

These volumes contain the proceedings of the conference held at Aarhus, Oxford and Madrid in September 2016 to mark the seventieth birthday of Nigel Hitchin, one of the world’s foremost geometers and Savilian Professor of Geometry at Oxford. The proceedings contain twenty-nine articles, including three by Fields medallists (Donaldson, Mori and Yau). The articles cover a wide range of topics in geometry and mathematical physics, including the following: Riemannian geometry, geometric analysis, special holonomy, integrable systems, dynamical systems, generalized complex structures, symplectic and Poisson geometry, low-dimensional topology, algebraic geometry, moduli spaces, Higgs bundles, geometric Langlands programme, mirror symmetry and string theory. These volumes will be of interest to researchers and graduate students both in geometry and mathematical physics.

Download Full-text

Towards creating a generalized complex event processing operator using FlinkCEP

Proceedings of the 15th ACM International Conference on Distributed and Event-based Systems ◽

10.1145/3465480.3467841 ◽

2021 ◽

Author(s):

Eleni Kougioumtzi ◽

Antonios Kontaxakis ◽

Antonios Deligiannakis ◽

Yannis Kotidis

Keyword(s):

Complex Event Processing ◽

Event Processing ◽

Generalized Complex

Download Full-text

Invariant generalized complex geometry on maximal flag manifolds and their moduli

Journal of Geometry and Physics ◽

10.1016/j.geomphys.2021.104108 ◽

2021 ◽

pp. 104108

Author(s):

Elizabeth Gasparim ◽

Fabricio Valencia ◽

Carlos Varea

Keyword(s):

Complex Geometry ◽

Flag Manifolds ◽

Generalized Complex

Download Full-text

Generalized almost even-Clifford manifolds and their twistor spaces

Complex Manifolds ◽

10.1515/coma-2020-0108 ◽

2021 ◽

Vol 8 (1) ◽

pp. 96-124

Author(s):

Luis Fernando Hernández-Moguel ◽

Rafael Herrera

Keyword(s):

Twistor Space ◽

Complex Structure ◽

Twistor Spaces ◽

Recent Interest ◽

Generalized Complex Structure ◽

Generalized Complex ◽

Space Construction ◽

Clifford Structures

Abstract Motivated by the recent interest in even-Clifford structures and in generalized complex and quaternionic geometries, we introduce the notion of generalized almost even-Clifford structure. We generalize the Arizmendi-Hadfield twistor space construction on even-Clifford manifolds to this setting and show that such a twistor space admits a generalized complex structure under certain conditions.

Download Full-text