scholarly journals HOW LARGE IS THE SHADOW OF A SYMPLECTIC BALL?

2013 ◽  
Vol 05 (01) ◽  
pp. 87-119 ◽  
Author(s):  
ALBERTO ABBONDANDOLO ◽  
ROSTISLAV MATVEYEV
Keyword(s):  
Vector Space ◽  
Unit Ball ◽  
Orthogonal Projection ◽  
Real Dimension ◽  
Symplectic Embedding ◽  
Dimensional Unit ◽  
Dimensional Ball ◽  
Symplectic Vector Space

Consider the image of the 2n-dimensional unit ball by a symplectic embedding into the standard symplectic vector space of dimension 2n. Its 2k-dimensional shadow is its orthogonal projection onto a complex subspace of real dimension 2k. Is it true that the volume of this 2k-dimensional shadow is at least the volume of the unit 2k-dimensional ball? This statement is trivially true when k = n, and when k = 1 it is a reformulation of Gromov's non-squeezing theorem. Therefore, this question can be considered as a middle-dimensional generalization of the non-squeezing theorem. We investigate the validity of this statement in the linear, nonlinear and perturbative setting.

scholarly journals Semi-embeddings of Banach spaces which are hereditarily c0

1983 ◽  
Vol 26 (2) ◽  
pp. 163-167 ◽  
Author(s):  
L. Drewnowski
Keyword(s):  
Banach Space ◽  
Linear Operator ◽  
Vector Space ◽  
Unit Ball ◽  
Banach Spaces ◽  
Continuous Linear Operator ◽  
Closed Unit Ball ◽  
Continuous Linear ◽  
Scattered Space ◽  
Complete Set

Following Lotz, Peck and Porta [9], a continuous linear operator from one Banach space into another is called a semi-embedding if it is one-to-one and maps the closed unit ball of the domain onto a closed (hence complete) set. (Below we shall allow the codomain to be an F-space, i.e., a complete metrisable topological vector space.) One of the main results established in [9] is that if X is a compact scattered space, then every semi-embedding of C(X) into another Banach space is an isomorphism ([9], Main Theorem, (a)⇒(b)).

scholarly journals Isomorphic exponential Weyl algebras

1991 ◽  
Vol 33 (1) ◽  
pp. 7-10 ◽  
Author(s):  
P. L. Robinson
Keyword(s):  
Vector Space ◽  
Weyl Algebra ◽  
Associative Algebras ◽  
Exponential Form ◽  
Canonical Commutation Relations ◽  
Commutation Relations ◽  
Weyl Algebras ◽  
The Subject ◽  
Symplectic Vector Space

Canonically associated to a real symplectic vector space are several associative algebras. The Weyl algebra (generated by the Heisenberg commutation relations) has been the subject of much study; see [1] for example. The exponential Weyl algebra (generated by the canonical commutation relations in exponential form) has been less well studied; see [8].

scholarly journals Equivariant Giambelli formula for the symplectic Grassmannians — Pfaffian Sum Formula

2015 ◽  
Vol DMTCS Proceedings, 27th... (Proceedings) ◽  
Author(s):  
Takeshi Ikeda ◽  
Tomoo Matsumura
Keyword(s):  
Vector Space ◽  
Closed Formula ◽  
International Audience ◽  
Sum Formula ◽  
Isotropic Subspaces ◽  
Espace Vectoriel ◽  
Symplectic Vector Space ◽  
Symplectic Grassmannians ◽  
Schubert Class

International audience We prove an explicit closed formula, written as a sum of Pfaffians, which describes each equivariant Schubert class for the Grassmannian of isotropic subspaces in a symplectic vector space On démontre une formule close explicite, écrite comme une somme de Pfaffiens, qui décrit toute classe de Schubert équivariante pour la Grassmannienne des sous-espaces isotropes dans un espace vectoriel symplectique.

scholarly journals Algebras of Toeplitz Operators on the n-Dimensional Unit Ball

2018 ◽  
Vol 13 (2) ◽  
pp. 493-524 ◽  
Author(s):  
Wolfram Bauer ◽  
Raffael Hagger ◽  
Nikolai Vasilevski
Keyword(s):  
Unit Ball ◽  
Toeplitz Operators ◽  
Algebras Of Toeplitz Operators ◽  
Dimensional Unit

A KNOTTED MINIMAL TREE

1999 ◽  
Vol 01 (01) ◽  
pp. 71-86
Author(s):  
KRYSTYNA KUPERBERG
Keyword(s):  
Unit Ball ◽  
Three Dimensional ◽  
Minimal Tree ◽  
Dimensional Unit ◽  
Finite Set ◽  
Set Of Points

There is a finite set of points on the boundary of the three-dimensional unit ball whose minimal tree is knotted. This example answers a problem posed by Michael Freedman.

scholarly journals Crepant resolutions and open strings

2019 ◽  
Vol 2019 (755) ◽  
pp. 191-245 ◽  
Author(s):  
Andrea Brini ◽  
Renzo Cavalieri ◽  
Dustin Ross
Keyword(s):  
Vector Space ◽  
Crepant Resolution ◽  
Complete Proof ◽  
Open Strings ◽  
Witten Theory ◽  
Crepant Resolutions ◽  
Symplectic Vector Space ◽  
Crepant Resolution Conjecture ◽  
Minimal Resolutions ◽  
Type Statement

AbstractIn the present paper, we formulate a Crepant Resolution Correspondence for open Gromov–Witten invariants (OCRC) of toric Lagrangian branes inside Calabi–Yau 3-orbifolds by encoding the open theories into sections of Givental’s symplectic vector space. The correspondence can be phrased as the identification of these sections via a linear morphism of Givental spaces. We deduce from this a Bryan–Graber-type statement for disk invariants, which we extend to arbitrary topologies in the Hard Lefschetz case. Motivated by ideas of Iritani, Coates–Corti–Iritani–Tseng and Ruan, we furthermore propose (1) a general form of the morphism entering the OCRC, which arises from a geometric correspondence between equivariant K-groups, and (2) an all-genus version of the OCRC for Hard Lefschetz targets. We provide a complete proof of both statements in the case of minimal resolutions of threefold {A_{n}}-singularities; as a necessary step of the proof we establish the all-genus closed Crepant Resolution Conjecture with descendents in its strongest form for this class of examples. Our methods rely on a new description of the quantum D-modules underlying the equivariant Gromov–Witten theory of this family of targets.

scholarly journals On the trivectors of a 6-dimensional symplectic vector space. IV

2013 ◽  
Vol 438 (5) ◽  
pp. 2405-2429 ◽  
Author(s):  
B. De Bruyn ◽  
M. Kwiatkowski
Keyword(s):  
Vector Space ◽  
Symplectic Vector Space
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