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Virtual Legendrian isotopy

Vladimir Chernov, Rustam Sadykov (2016)

Fundamenta Mathematicae

An elementary stabilization of a Legendrian knot L in the spherical cotangent bundle ST*M of a surface M is a surgery that results in attaching a handle to M along two discs away from the image in M of the projection of the knot L. A virtual Legendrian isotopy is a composition of stabilizations, destabilizations and Legendrian isotopies. A class of virtual Legendrian isotopy is called a virtual Legendrian knot. In contrast to Legendrian knots, virtual Legendrian knots enjoy the...

Weak symplectic fillings and holomorphic curves

Klaus Niederkrüger, Chris Wendl (2011)

Annales scientifiques de l'École Normale Supérieure

We prove several results on weak symplectic fillings of contact 3 -manifolds, including: (1) Every weak filling of any planar contact manifold can be deformed to a blow up of a Stein filling. (2) Contact manifolds that have fully separating planar torsion are not weakly fillable—this gives many new examples of contact manifolds without Giroux torsion that have no weak fillings. (3) Weak fillability is preserved under splicing of contact manifolds along symplectic pre-Lagrangian tori—this gives many...

Weyl quantization for the semidirect product of a compact Lie group and a vector space

Benjamin Cahen (2009)

Commentationes Mathematicae Universitatis Carolinae

Let G be the semidirect product V K where K is a semisimple compact connected Lie group acting linearly on a finite-dimensional real vector space V . Let 𝒪 be a coadjoint orbit of G associated by the Kirillov-Kostant method of orbits with a unitary irreducible representation π of G . We consider the case when the corresponding little group H is the centralizer of a torus of K . By dequantizing a suitable realization of π on a Hilbert space of functions on n where n = dim ( K / H ) , we construct a symplectomorphism between...

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