scholarly journals Higher-dimensional contact manifolds with infinitely many Stein fillings

2018 ◽  
Vol 370 (7) ◽  
pp. 5033-5050 ◽  
Author(s):  
Takahiro Oba
Keyword(s):  
Contact Manifolds ◽  
Stein Fillings ◽  
Higher Dimensional

scholarly journals Weak and strong fillability of higher dimensional contact manifolds

2012 ◽  
Vol 192 (2) ◽  
pp. 287-373 ◽  
Author(s):  
Patrick Massot ◽  
Klaus Niederkrüger ◽  
Chris Wendl
Keyword(s):  
Contact Manifolds ◽  
Higher Dimensional

scholarly journals THE WEINSTEIN CONJECTURE IN THE PRESENCE OF SUBMANIFOLDS HAVING A LEGENDRIAN FOLIATION

2011 ◽  
Vol 03 (04) ◽  
pp. 405-421 ◽  
Author(s):  
KLAUS NIEDERKRÜGER ◽  
ANA RECHTMAN
Keyword(s):  
Projective Space ◽  
Holomorphic Curves ◽  
Real Projective Space ◽  
Contact Manifolds ◽  
Connected Sum ◽  
Novel Technique ◽  
Weinstein Conjecture ◽  
Higher Dimensional

Helmut Hofer introduced in 1993 a novel technique based on holomorphic curves to prove the Weinstein conjecture. Among the cases where these methods apply are all contact 3-manifolds (M, ξ) with π2(M) ≠ 0. We modify Hofer's argument to prove the Weinstein conjecture for some examples of higher-dimensional contact manifolds. In particular, we are able to show that the connected sum with a real projective space always has a closed contractible Reeb orbit.

scholarly journals SFT COMPUTATIONS AND INTERSECTION THEORY IN HIGHER-DIMENSIONAL CONTACT MANIFOLDS

2021 ◽  
pp. 1-52
Author(s):  
Agustin Moreno
Keyword(s):  
Field Theory ◽  
Intersection Theory ◽  
Holomorphic Curves ◽  
Perturbation Scheme ◽  
Contact Manifolds ◽  
Higher Dimensional ◽  
Symplectic Field Theory ◽  
Phd Thesis ◽  
Symplectic Cobordisms

Abstract I construct infinitely many nondiffeomorphic examples of $5$ -dimensional contact manifolds which are tight, admit no strong fillings and do not have Giroux torsion. I obtain obstruction results for symplectic cobordisms, for which I give a proof not relying on the polyfold abstract perturbation scheme for Symplectic Field Theory (SFT). These results are part of my PhD thesis [23], and are the first applications of higher-dimensional Siefring intersection theory for holomorphic curves and hypersurfaces, as outlined in [23, 24], as a prequel to [30].

scholarly journals Planarity in Higher-Dimensional Contact Manifolds

2020 ◽  
Author(s):  
Bahar Acu ◽  
Agustin Moreno
Keyword(s):  
Higher Dimensions ◽  
Symplectic Manifolds ◽  
Contact Form ◽  
Contact Manifolds ◽  
Contact Type ◽  
Weinstein Conjecture ◽  
Higher Dimensional ◽  
Alternative Approach ◽  
Weak Contact ◽  
Planar Contact

Abstract We obtain several results for (iterated) planar contact manifolds in higher dimensions. (1) Iterated planar contact manifolds are not weakly symplectically co-fillable. This generalizes a 3D result of Etnyre [ 14] to a higher-dimensional setting, where the notion of weak fillability is that due to Massot-Niederkrüger-Wendl [ 38]. (2) They do not arise as nonseparating weak contact-type hypersurfaces in closed symplectic manifolds. This generalizes a result by Albers-Bramham-Wendl [ 4]. (3) They satisfy the Weinstein conjecture, that is, every contact form admits a closed Reeb orbit. This is proved by an alternative approach as that of [ 2] and is a higher-dimensional generalization of a result of Abbas-Cieliebak-Hofer [ 1]. The results follow as applications from a suitable symplectic handle attachment, which bears some independent interest.

scholarly journals A note on Stein fillings of contact manifolds

2008 ◽  
Vol 15 (6) ◽  
pp. 1127-1132 ◽  
Author(s):  
Anar Akhmedov ◽  
John B. Etnyre ◽  
Thomas E. Mark ◽  
Ivan Smith
Keyword(s):  
Contact Manifolds ◽  
Stein Fillings

scholarly journals Symplectic cobordisms and the strong Weinstein conjecture

2012 ◽  
Vol 153 (2) ◽  
pp. 261-279 ◽  
Author(s):  
HANSJÖRG GEIGES ◽  
KAI ZEHMISCH
Keyword(s):  
Moduli Spaces ◽  
Quantitative Character ◽  
Contact Manifolds ◽  
Symplectic Capacity ◽  
Contact Type ◽  
Weinstein Conjecture ◽  
Cotangent Bundles ◽  
Higher Dimensional ◽  
Definition Of ◽  
Symplectic Cobordisms

AbstractWe study holomorphic spheres in certain symplectic cobordisms and derive information about periodic Reeb orbits in the concave end of these cobordisms from the non-compactness of the relevant moduli spaces. We use this to confirm the strong Weinstein conjecture (predicting the existence of null-homologous Reeb links) for various higher-dimensional contact manifolds, including contact type hypersurfaces in subcritical Stein manifolds and in some cotangent bundles. The quantitative character of this result leads to the definition of a symplectic capacity.

Spectroscopy-Based Mapping with Scanning Microwave Impedance Microscopy

2018 ◽  
Author(s):  
Peter De Wolf ◽  
Zhuangqun Huang ◽  
Bede Pittenger
Keyword(s):  
Single Point ◽  
Electrical Characterization ◽  
Principal Component ◽  
High Sensitivity ◽  
Data Cube ◽  
Nanometer Scale ◽  
Learning Approaches ◽  
Data Set ◽  
3D Data ◽  
Higher Dimensional

Abstract Methods are available to measure conductivity, charge, surface potential, carrier density, piezo-electric and other electrical properties with nanometer scale resolution. One of these methods, scanning microwave impedance microscopy (sMIM), has gained interest due to its capability to measure the full impedance (capacitance and resistive part) with high sensitivity and high spatial resolution. This paper introduces a novel data-cube approach that combines sMIM imaging and sMIM point spectroscopy, producing an integrated and complete 3D data set. This approach replaces the subjective approach of guessing locations of interest (for single point spectroscopy) with a big data approach resulting in higher dimensional data that can be sliced along any axis or plane and is conducive to principal component analysis or other machine learning approaches to data reduction. The data-cube approach is also applicable to other AFM-based electrical characterization modes.

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