scholarly journals Fillings and fittings of unit cotangent bundles of odd-dimensional spheres

2019 ◽  
Author(s):  
Myeonggi Kwon ◽  
Kai Zehmisch
Keyword(s):  
Cotangent Bundle ◽  
Cotangent Bundles ◽  
Disc Bundle

AbstractWe introduce the concept of fittings to symplectic fillings of the unit cotangent bundle of odd-dimensional spheres. Assuming symplectic asphericity we show that all fittings are diffeomorphic to the respective unit co-disc bundle.

scholarly journals STRINGS IN SPACE-TIME COTANGENT BUNDLE AND T-DUALITY

1995 ◽  
Vol 10 (04) ◽  
pp. 323-329 ◽  
Author(s):  
C. KLIMČÍK ◽  
P. ŠEVERA
Keyword(s):  
Cotangent Bundle ◽  
Space Time ◽  
Geometric Description ◽  
Cotangent Bundles

A simple geometric description of T-duality is given by identifying the cotangent bundles of the original and the dual manifold. Strings propagate naturally in the cotangent bundle and the original and the dual string phase spaces are obtained by different projections. Buscher's transformation follows readily and it is literally projective. As an application of the formalism, we prove that the duality is a symplectomorphism of the string phase spaces.

scholarly journals Invariance of symplectic cohomology and twisted cotangent bundles over surfaces

2020 ◽  
Vol 31 (09) ◽  
pp. 2050070
Author(s):  
Gabriele Benedetti ◽  
Alexander F. Ritter
Keyword(s):  
Symplectic Form ◽  
Cotangent Bundle ◽  
Local System ◽  
Symplectic Manifolds ◽  
Existence Results ◽  
Open Convex ◽  
Floer Theory ◽  
Cotangent Bundles ◽  
Sample Application ◽  
Symplectic Cohomology

We prove that symplectic cohomology for open convex symplectic manifolds is invariant when the symplectic form undergoes deformations which may be nonexact and noncompactly supported, provided one uses the correct local system of coefficients in Floer theory. As a sample application beyond the Liouville setup, we describe in detail the symplectic cohomology for disc bundles in the twisted cotangent bundle of surfaces, and we deduce existence results for periodic magnetic geodesics on surfaces. In particular, we show the existence of geometrically distinct orbits by exploiting properties of the BV-operator on symplectic cohomology.

scholarly journals On horizontal and complete lifts from a manifold withfλ(7,1)-structure to its cotangent bundle

2005 ◽  
Vol 2005 (8) ◽  
pp. 1291-1297 ◽  
Author(s):  
Lovejoy S. Das ◽  
Ram Nivas ◽  
Virendra Nath Pathak
Keyword(s):  
Cotangent Bundle ◽  
Cotangent Bundles

The horizontal and complete lifts from a manifoldMnto its cotangent bundlesT∗(Mn)were studied by Yano and Ishihara, Yano and Patterson, Nivas and Gupta, Dambrowski, and many others. The purpose of this paper is to use certain methods by whichfλ(7,1)-structure inMncan be extended toT∗(Mn). In particular, we have studied horizontal and complete lifts offλ(7,1)-structure from a manifold to its cotangent bundle.

scholarly journals Quantization commutes with singular reduction: Cotangent bundles of compact Lie groups

2019 ◽  
Vol 31 (06) ◽  
pp. 1950016
Author(s):  
Jord Boeijink ◽  
Klaas Landsman ◽  
Walter van Suijlekom
Keyword(s):  
Hilbert Space ◽  
Dirac Operator ◽  
Cotangent Bundle ◽  
Geometric Quantization ◽  
Compact Lie Groups ◽  
Kähler Structure ◽  
Momentum Map ◽  
Cotangent Bundles ◽  
Reduction Problem ◽  
Mathematical Literature

We analyze the ‘quantization commutes with reduction’ problem (first studied in physics by Dirac, and known in the mathematical literature also as the Guillemin–Sternberg Conjecture) for the conjugate action of a compact connected Lie group [Formula: see text] on its own cotangent bundle [Formula: see text]. This example is interesting because the momentum map is not proper and the ensuing symplectic (or Marsden–Weinstein quotient) [Formula: see text] is typically singular.In the spirit of (modern) geometric quantization, our quantization of [Formula: see text] (with its standard Kähler structure) is defined as the kernel of the Dolbeault–Dirac operator (or, equivalently, the spin[Formula: see text]–Dirac operator) twisted by the pre-quantum line bundle. We show that this quantization of [Formula: see text] reproduces the Hilbert space found earlier by Hall (2002) using geometric quantization based on a holomorphic polarization. We then define the quantization of the singular quotient [Formula: see text] as the kernel of the twisted Dolbeault–Dirac operator on the principal stratum, and show that quantization commutes with reduction in the sense that either way one obtains the same Hilbert space [Formula: see text].

scholarly journals -rigidity of Lagrangian submanifolds and punctured holomorphic disks in the cotangent bundle

2021 ◽  
Vol 157 (11) ◽  
pp. 2433-2493
Author(s):  
Cedric Membrez ◽  
Emmanuel Opshtein
Keyword(s):  
Cotangent Bundle ◽  
Symplectic Geometry ◽  
Homology Class ◽  
Lagrangian Submanifolds ◽  
Area Spectrum ◽  
Zero Section ◽  
Integral Homology ◽  
Cotangent Bundles ◽  
Maslov Class ◽  
Holomorphic Disks

Abstract Our main result is the $\mathbb {\mathcal {C}}^{0}$ -rigidity of the area spectrum and the Maslov class of Lagrangian submanifolds. This relies on the existence of punctured pseudoholomorphic disks in cotangent bundles with boundary on the zero section, whose boundaries represent any integral homology class. We discuss further applications of these punctured disks in symplectic geometry.

scholarly journals Lagrangian exotic spheres

2016 ◽  
Vol 08 (03) ◽  
pp. 375-397 ◽  
Author(s):  
Tobias Ekholm ◽  
Thomas Kragh ◽  
Ivan Smith
Keyword(s):  
Cotangent Bundle ◽  
Zero Section ◽  
Homotopy Formula ◽  
Connected Sum ◽  
Cotangent Bundles ◽  
Sum Formula ◽  
Lagrangian Embedding ◽  
Exotic Spheres

Let [Formula: see text]. We prove that the cotangent bundles [Formula: see text] and [Formula: see text] of oriented homotopy [Formula: see text]-spheres [Formula: see text] and [Formula: see text] are symplectomorphic only if [Formula: see text], where [Formula: see text] denotes the group of oriented homotopy [Formula: see text]-spheres under connected sum, [Formula: see text] denotes the subgroup of those that bound a parallelizable [Formula: see text]-manifold, and where [Formula: see text] denotes [Formula: see text] with orientation reversed. We further show that if [Formula: see text] and [Formula: see text] admits a Lagrangian embedding in [Formula: see text], then [Formula: see text]. The proofs build on [1] and [18] in combination with a new cut-and-paste argument; that also yields some interesting explicit exact Lagrangian embeddings, for instance of the sphere [Formula: see text] into the plumbing [Formula: see text] of cotangent bundles of certain exotic spheres. As another application, we show that there are re-parametrizations of the zero-section in the cotangent bundle of a sphere that are not Hamiltonian isotopic (as maps rather than as submanifolds) to the original zero-section.

scholarly journals A Study on the Para-Holomorphic Sectional Curvature of Para-Kähler Cotangent Bundles

2015 ◽  
Vol 61 (1) ◽  
pp. 253-262
Author(s):  
S. L. Druţă-Romaniuc
Keyword(s):  
Sectional Curvature ◽  
Cotangent Bundle ◽  
Total Space ◽  
Holomorphic Sectional Curvature ◽  
Kähler Structure ◽  
Nonzero Constant ◽  
Cotangent Bundles

Abstract We obtain the conditions under which the total space T *M of the cotangent bundle, endowed with a natural diagonal para-Kähler structure (G, P), has constant para-holomorphic sectional curvature. Moreover we prove that (T *M,G, P) cannot have nonzero constant para-holomorphic sectional curvature.

scholarly journals Infinitely many leaf-wise intersections on cotangent bundles

2012 ◽  
Vol 30 (2) ◽  
pp. 168-181 ◽  
Author(s):  
Peter Albers ◽  
Urs Frauenfelder
Keyword(s):  
Cotangent Bundles
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