scholarly journals Presentations of Cluster Modular Groups and Generation by Cluster Dehn Twists

2020 ◽  
Author(s):  
Tsukasa Ishibashi ◽  
Keyword(s):  
Dehn Twists ◽  
Modular Groups

Pseudo-Anosov Theory

2017 ◽  
Author(s):  
Benson Farb ◽  
Dan Margalit
Keyword(s):  
Braid Groups ◽  
Intersection Numbers ◽  
Branched Covers ◽  
Algebraic Integers ◽  
Dehn Twists ◽  
Mapping Classes ◽  
Dynamical Properties

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.

Determination of the Ternary Modular Groups

1905 ◽  
Vol 27 (2) ◽  
pp. 189 ◽  
Author(s):  
Leonard Eugene Dickson
Keyword(s):  
Modular Groups

scholarly journals Effectiveness of lumbar orthoses in low back pain: Review of the literature and our results

2018 ◽  
Vol 10 (4) ◽  
Author(s):  
Cordelia Schott ◽  
Sonja Zirke ◽  
Jillian Marie Schmelzle ◽  
Christel Kaiser ◽  
Lluis Aguilar I Fernández
Keyword(s):  
Low Back Pain ◽  
Back Pain ◽  
Randomized Study ◽  
Cost Of Care ◽  
Modular System ◽  
Low Back ◽  
Modular Systems ◽  
Frequency Of Use ◽  
Modular Groups ◽  
The Cost

Back pain and diseases of the spine are today a health disorder of outstanding epidemiological, medical, and health economic importance. The cost of care for patients with lumbosciatic complaints are steadily increasing. Accordingly, the guidelines and treatments are constantly renewed. One concept is the orthotic care. In the following we want to give an overview of the literature and the effectiveness of lumbar orthoses in low back pain supplemented by our own data. A prospective randomized study with 230 patients, divided into three groups, each with two subgroups. Three Orthoses by the TIGGES-Zours GmbH were prescribed; a demountable two-step lumbar orthosis, three-step bridging orthosis and a four-step flexion orthosis modular system. Each were compared to the nonmodular equivalent. All six groups showed improvement in pain intensity and functional capacity at 6 and 12 weeks. The modular groups were found to have improvement in the frequency of use. The subjective effectiveness and sensitivity for the modular and non-modular groups was assessed as being good. In the literature, there are no clear guidelines for an orthotic supply. The studies do not seem to be meaningful and universal due to the difficult ascertainability of pain. There is a need for further research here. Nevertheless, the authors of this review are of the opinion that the implementation of trunk orthoses is void of side effects and beneficial to patients. The modular systems seem to have an advantage as well as higher patient satisfaction.

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
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