scholarly journals Dehn twists on nonorientable surfaces

2006 ◽  
Vol 189 (2) ◽  
pp. 117-147 ◽  
Author(s):  
Michał Stukow
Keyword(s):  
Dehn Twists ◽  
Nonorientable Surfaces

scholarly journals Roots of Dehn twists on nonorientable surfaces

2019 ◽  
Vol 28 (12) ◽  
pp. 1950077
Author(s):  
Anna Parlak ◽  
Michał Stukow
Keyword(s):  
Mapping Class Group ◽  
Class Group ◽  
Mapping Class ◽  
Maximal Degree ◽  
Simple Arithmetic ◽  
Nonorientable Surface ◽  
Dehn Twists ◽  
Nonorientable Surfaces ◽  
Genus Formula ◽  
Orientable Surfaces

Margalit and Schleimer observed that Dehn twists on orientable surfaces have nontrivial roots. We investigate the problem of roots of a Dehn twist [Formula: see text] about a nonseparating circle [Formula: see text] in the mapping class group [Formula: see text] of a nonorientable surface [Formula: see text] of genus [Formula: see text]. We explore the existence of roots and, following the work of McCullough, Rajeevsarathy and Monden, give a simple arithmetic description of their conjugacy classes. We also study roots of maximal degree and prove that if we fix an odd integer [Formula: see text], then for each sufficiently large [Formula: see text], [Formula: see text] has a root of degree [Formula: see text] in [Formula: see text]. Moreover, for any possible degree [Formula: see text], we provide explicit expressions for a particular type of roots of Dehn twists about nonseparating circles in [Formula: see text].

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.

scholarly journals Automorphisms of curve complexes on nonorientable surfaces

2014 ◽  
Vol 8 (1) ◽  
pp. 39-68 ◽  
Author(s):  
Ferihe Atalan ◽  
Mustafa Korkmaz
Keyword(s):  
Nonorientable Surfaces ◽  
Curve Complexes

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 Existence of minimal flows on nonorientable surfaces

2017 ◽  
Vol 37 (8) ◽  
pp. 4191-4211
Author(s):  
José Ginés Espín Buendía ◽  
◽  
Daniel Peralta-salas ◽  
Gabriel Soler López ◽  
◽  
...  
Keyword(s):  
Nonorientable Surfaces

The logarithms of Dehn twists

10.4171/qt/54 ◽  
2014 ◽  
Vol 5 (3) ◽  
pp. 347-423 ◽  
Author(s):  
Nariya Kawazumi ◽  
Yusuke Kuno
Keyword(s):  
Dehn Twists

scholarly journals Centralisers of Dehn twist automorphisms of free groups

2015 ◽  
Vol 159 (1) ◽  
pp. 89-114 ◽  
Author(s):  
MORITZ RODENHAUSEN ◽  
RICHARD D. WADE
Keyword(s):  
Free Group ◽  
Finite Index ◽  
Free Groups ◽  
Dehn Twist ◽  
Classifying Space ◽  
Dehn Twists ◽  
Automorphisms Of Free Groups

AbstractWe refine Cohen and Lustig's description of centralisers of Dehn twists of free groups. We show that the centraliser of a Dehn twist of a free group has a subgroup of finite index that has a finite classifying space. We describe an algorithm to find a presentation of the centraliser. We use this algorithm to give an explicit presentation for the centraliser of a Nielsen automorphism in Aut(Fn). This gives restrictions to actions of Aut(Fn) on CAT(0) spaces.

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