scholarly journals Examples of Non-trivial Contact Mapping Classes in all Dimensions

2016 ◽  
Vol 2016 (15) ◽  
pp. 4784-4806 ◽  
Author(s):  
Patrick Massot ◽  
Niederkrüger Klaus
Author(s):  
Benson Farb ◽  
Dan Margalit

This chapter focuses on the construction as well as the algebraic and dynamical properties of pseudo-Anosov homeomorphisms. It first presents five different constructions of pseudo-Anosov mapping classes: branched covers, constructions via Dehn twists, homological criterion, Kra's construction, and a construction for braid groups. It then proves a few fundamental facts concerning stretch factors of pseudo-Anosov homeomorphisms, focusing on the theorem that pseudo-Anosov stretch factors are algebraic integers. It also considers the spectrum of pseudo-Anosov stretch factors, along with the special properties of those measured foliations that are the stable (or unstable) foliations of some pseudo-Anosov homeomorphism. Finally, it describes the orbits of a pseudo-Anosov homeomorphism as well as lengths of curves and intersection numbers under iteration.


2004 ◽  
Vol 52 (Suppl 2) ◽  
pp. S357.3-S357
Author(s):  
D. Xing ◽  
F. G. Devecchi ◽  
T. R. Staley ◽  
D. S. Glassman ◽  
J. B. Martins

Author(s):  
Martin Eichenlaub ◽  
Bjoern Mueller-Edenborn ◽  
Jan Minners ◽  
Martin Allgeier ◽  
Heiko Lehrmann ◽  
...  

Abstract Background Relevant atrial cardiomyopathy (ACM), defined as a left atrial (LA) low-voltage area ≥ 2 cm2 at 0.5 mV threshold on endocardial contact mapping, is associated with new-onset atrial fibrillation (AF), higher arrhythmia recurrence rates after pulmonary vein isolation (PVI), and an increased risk of stroke. The current study aimed to assess two non-invasive echocardiographic parameters, LA emptying fraction (EF) and LA longitudinal strain (LAS, during reservoir (LASr), conduit (LAScd) and contraction phase (LASct)) for the diagnosis of ACM and prediction of arrhythmia outcome after PVI. Methods We prospectively enrolled 60 consecutive, ablation-naive patients (age 66 ± 9 years, 80% males) with persistent AF. In 30 patients (derivation cohort), LA-EF and LAS cut-off values for the presence of relevant ACM (high-density endocardial contact mapping in sinus rhythm prior to PVI at 3000 ± 1249 sites) were established in sinus rhythm and tested in a validation cohort (n = 30). Arrhythmia recurrence within 12 months was documented using 72-h Holter electrocardiograms. Results An LA-EF of < 34% predicted ACM with an area under the curve (AUC) of 0.846 (sensitivity 69.2%, specificity 76.5%) similar to a LASr < 23.5% (AUC 0.878, sensitivity 92.3%, specificity 82.4%). In the validation cohort, these cut-offs established the correct diagnosis of ACM in 76% of patients (positive predictive values 87%/93% and negative predictive values 73%/75%, respectively). Arrhythmia recurrence in the entire cohort was significantly more frequent in patients with LA-EF < 34% and LASr < 23.5% (56% vs. 29% and 55% vs. 26%, both p < 0.05). Conclusion The echocardiographic parameters LA-EF and LAS allow accurate, non-invasive diagnosis of ACM and prediction of arrhythmia recurrence after PVI. Graphic abstract


EP Europace ◽  
2003 ◽  
Vol 4 (Supplement_2) ◽  
pp. B166-B166
Author(s):  
L. Leite ◽  
K.H. Monahan ◽  
A. Sarabanda ◽  
L. Peterson ◽  
C.M. Bluhm ◽  
...  

EP Europace ◽  
2014 ◽  
Vol 17 (1) ◽  
pp. 108-116 ◽  
Author(s):  
N. Trevisi ◽  
J. Silberbauer ◽  
A. Radinovic ◽  
R. Bavila ◽  
S. Sala ◽  
...  

EP Europace ◽  
2010 ◽  
Vol 12 (6) ◽  
pp. 881-889 ◽  
Author(s):  
Jim Pouliopoulos ◽  
Gopal Sivagangabalan ◽  
Michael A. Barry ◽  
Aravinda Thiagalingam ◽  
Kaimin Huang ◽  
...  
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