scholarly journals Open books for Boothby-Wang bundles, fibered Dehn twists and the mean Euler characteristic

2014 ◽  
Vol 12 (2) ◽  
pp. 379-426 ◽  
Author(s):  
River Chiang ◽  
Fan Ding ◽  
Otto van Koert
Keyword(s):  
Euler Characteristic ◽  
Open Books ◽  
Dehn Twists ◽  
The Mean

scholarly journals Identification and isotropy characterization of deformed random fields through excursion sets

2018 ◽  
Vol 50 (3) ◽  
pp. 706-725
Author(s):  
Julie Fournier
Keyword(s):  
Random Field ◽  
Euler Characteristic ◽  
Random Fields ◽  
Weak Form ◽  
Invariance Property ◽  
Basic Domain ◽  
Excursion Sets ◽  
The Mean ◽  
Isotropic Random

Abstract A deterministic application θ:ℝ2→ℝ2 deforms bijectively and regularly the plane and allows the construction of a deformed random field X∘θ:ℝ2→ℝ from a regular, stationary, and isotropic random field X:ℝ2→ℝ. The deformed field X∘θ is, in general, not isotropic (and not even stationary), however, we provide an explicit characterization of the deformations θ that preserve the isotropy. Further assuming that X is Gaussian, we introduce a weak form of isotropy of the field X∘θ, defined by an invariance property of the mean Euler characteristic of some of its excursion sets. We prove that deformed fields satisfying this property are strictly isotropic. In addition, we are able to identify θ, assuming that the mean Euler characteristic of excursion sets of X∘θ over some basic domain is known.

scholarly journals Iterated index and the mean Euler characteristic

2015 ◽  
Vol 07 (03) ◽  
pp. 453-481 ◽  
Author(s):  
Viktor L. Ginzburg ◽  
Yusuf Gören
Keyword(s):  
Euler Characteristic ◽  
Contact Manifold ◽  
Finsler Metric ◽  
Topological Invariants ◽  
Closed Geodesics ◽  
Lefschetz Numbers ◽  
Local Case ◽  
The Mean ◽  
Standard Contact ◽  
Global And Local

The aim of the paper is three-fold. We begin by proving a formula, both global and local versions, relating the number of periodic orbits of an iterated map and the Lefschetz numbers, or indices in the local case, of its iterations. This formula is then used to express the mean Euler characteristic (MEC) of a contact manifold in terms of local, purely topological, invariants of closed Reeb orbits, without any non-degeneracy assumption on the orbits. Finally, turning to applications of the local MEC formula to dynamics, we use it to reprove a theorem asserting the existence of at least two closed Reeb orbits on the standard contact S3 (by Cristofaro–Gardiner and Hutchings in the most general form) and the existence of at least two closed geodesics for a Finsler metric on S2 (Bangert and Long).

scholarly journals Simplicial Homology of Random Configurations

2014 ◽  
Vol 46 (02) ◽  
pp. 325-347 ◽  
Author(s):  
L. Decreusefond ◽  
E. Ferraz ◽  
H. Randriambololona ◽  
A. Vergne
Keyword(s):  
Poisson Process ◽  
Euler Characteristic ◽  
Poisson Point Process ◽  
Concentration Inequality ◽  
Dimensional Torus ◽  
Simplicial Homology ◽  
First Order ◽  
Tail Distribution ◽  
The Mean ◽  
Stein Method

Given a Poisson process on a d-dimensional torus, its random geometric simplicial complex is the complex whose vertices are the points of the Poisson process and simplices are given by the C̆ech complex associated to the coverage of each point. By means of Malliavin calculus, we compute explicitly the three first-order moments of the number of k-simplices, and provide a way to compute higher-order moments. Then we derive the mean and the variance of the Euler characteristic. Using the Stein method, we estimate the speed of convergence of the number of occurrences of any connected subcomplex as it converges towards the Gaussian law when the intensity of the Poisson point process tends to infinity. We use a concentration inequality for Poisson processes to find bounds for the tail distribution of the Betti number of first order and the Euler characteristic in such simplicial complexes.

scholarly journals Simplicial Homology of Random Configurations

2014 ◽  
Vol 46 (2) ◽  
pp. 325-347 ◽  
Author(s):  
L. Decreusefond ◽  
E. Ferraz ◽  
H. Randriambololona ◽  
A. Vergne
Keyword(s):  
Poisson Process ◽  
Euler Characteristic ◽  
Poisson Point Process ◽  
Concentration Inequality ◽  
Dimensional Torus ◽  
Simplicial Homology ◽  
First Order ◽  
Tail Distribution ◽  
The Mean ◽  
Stein Method

Given a Poisson process on a d-dimensional torus, its random geometric simplicial complex is the complex whose vertices are the points of the Poisson process and simplices are given by the C̆ech complex associated to the coverage of each point. By means of Malliavin calculus, we compute explicitly the three first-order moments of the number of k-simplices, and provide a way to compute higher-order moments. Then we derive the mean and the variance of the Euler characteristic. Using the Stein method, we estimate the speed of convergence of the number of occurrences of any connected subcomplex as it converges towards the Gaussian law when the intensity of the Poisson point process tends to infinity. We use a concentration inequality for Poisson processes to find bounds for the tail distribution of the Betti number of first order and the Euler characteristic in such simplicial complexes.

scholarly journals On the mean Euler characteristic and mean Betti’s numbers of the Ising model with arbitrary spin

2006 ◽  
Vol 2006 (03) ◽  
pp. P03011-P03011 ◽  
Author(s):  
Philippe Blanchard ◽  
Christophe Dobrovolny ◽  
Daniel Gandolfo ◽  
Jean Ruiz
Keyword(s):  
Ising Model ◽  
Euler Characteristic ◽  
Arbitrary Spin ◽  
The Mean

scholarly journals Non-fillable invariant contact structures on principal circle bundles and left-handed twists

2016 ◽  
Vol 27 (03) ◽  
pp. 1650024 ◽  
Author(s):  
River Chiang ◽  
Fan Ding ◽  
Otto van Koert
Keyword(s):  
Circle Action ◽  
Contact Structures ◽  
Contact Manifolds ◽  
Open Books ◽  
Dehn Twists ◽  
Left Handed ◽  
Circle Bundles

We define symplectic fractional twists, which subsume Dehn twists and fibered twists and use these in open books to investigate contact structures. The resulting contact structures are invariant under a circle action, and share several similarities with the invariant contact structures that were studied by Lutz and Giroux. We show that left-handed fractional twists often give rise to “algebraically overtwisted” contact manifolds, a certain class of non-fillable contact manifolds.

scholarly journals On the mean Euler characteristic of contact manifolds

2014 ◽  
Vol 25 (05) ◽  
pp. 1450046 ◽  
Author(s):  
Jacqueline Espina
Keyword(s):  
Euler Characteristic ◽  
Contact Structure ◽  
Broad Class ◽  
Contact Manifolds ◽  
Contact Surgery ◽  
The Mean

We express the mean Euler characteristic (MEC) of a contact structure in terms of the mean indices of closed Reeb orbits for a broad class of contact manifolds, the so-called asymptotically finite contact manifolds. We show that this class is closed under subcritical contact surgery and examine the behavior of the MEC under such surgery. To this end, we revisit the notion of index-positivity for contact forms. We also obtain an expression for the MEC in the Morse–Bott case.

scholarly journals On the Mean Euler Characteristic of Gorenstein Toric Contact Manifolds

2018 ◽  
Vol 2020 (14) ◽  
pp. 4465-4495 ◽  
Author(s):  
Miguel Abreu ◽  
Leonardo Macarini
Keyword(s):  
Euler Characteristic ◽  
Chern Class ◽  
Contact Manifold ◽  
Contact Manifolds ◽  
Toric Diagram ◽  
The Mean ◽  
Toric Contact Manifolds ◽  
Symplectic Filling

Abstract We prove that the mean Euler characteristic of a Gorenstein toric contact manifold, that is, a good toric contact manifold with zero 1st Chern class, is equal to half the normalized volume of the corresponding toric diagram and give some applications. A particularly interesting one, obtained using a result of Batyrev and Dais, is the following: twice the mean Euler characteristic of a Gorenstein toric contact manifold is equal to the Euler characteristic of any crepant toric symplectic filling, that is, any toric symplectic filling with zero 1st Chern class.

scholarly journals Displaceability and the mean Euler characteristic

2012 ◽  
Vol 52 (4) ◽  
pp. 797-815 ◽  
Author(s):  
Urs Frauenfelder ◽  
Felix Schlenk ◽  
Otto van Koert
Keyword(s):  
Euler Characteristic ◽  
The Mean
Sign in / Sign up

Export Citation Format

Share Document