1 - 10 of 13 articles
We adapt the notion of generating functions for lagrangian submanifolds to symplectic microgeometry. We show that a symplectic micromorphism always admits a global generating function. As an application, we describe hamiltonian flows as special symplectic micromorphisms whose local generating...
We show that the blow-up of a generalized Kähler 4-manifold in a nondegenerate complex point admits a generalized Kähler metric. As with the blow-up of complex surfaces, this metric may be chosen to coincide with the original outside a tubular neighbourhood of the exceptional divisor. To...
We remark that the equations underlying the notion of generalized complex structure have simple geometric meaning when passing to Lie algebroids/groupoids.
Motivated by the problem of longitudinal data assimilation, e.g., in the registration of a sequence of images, we develop the higher-order framework for Lagrangian and Hamiltonian reduction by symmetry in geometric mechanics. In particular, we obtain the reduced variational principles and the...
In this short note we give a complete characterization of a certain class of compact corank one Poisson manifolds, those equipped with a closed one-form defining the symplectic foliation and a closed two-form extending the symplectic form on each leaf. If such a manifold has a compact leaf, then...
We study Nijenhuis structures on Courant algebroids in terms of the canonical Poisson bracket on their symplectic realizations. We prove that the Nijenhuis torsion of a skew-symmetric endomorphism N of a Courant algebroid is skewsymmetric if N
2 is proportional to the identity, and only in this...
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...
We review several well-known operads of compactified configuration spaces and construct several new such operads,
, in the category of smooth manifolds with corners whose complexes of fundamental chains give us (i) the 2-coloured operad of A
∞-algebras and their homotopy morphisms, (ii)...
Hans Duistermaat was scheduled to lecture in the 2010 School on Poisson Geometry at IMPA, but passed away suddenly. This is a record of a talk I gave at the 2010 Conference on Poisson Geometry (the week after the School) to share some of my memories of him and to give a brief assessment of his...
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