scholarly journals Nielsen theory, braids and fixed points of surface homeomorphisms

2002 ◽  
Vol 117 (2) ◽  
pp. 199-230 ◽  
Author(s):  
John Guaschi
Keyword(s):  
Fixed Points ◽  
Nielsen Theory ◽  
Surface Homeomorphisms

scholarly journals Recurrent surface homeomorphisms

1998 ◽  
Vol 124 (1) ◽  
pp. 161-168 ◽  
Author(s):  
B. KOLEV ◽  
M.-C. PÉROUÈME
Keyword(s):  
Fixed Points ◽  
Euler Characteristic ◽  
Compact Surface ◽  
Surface Homeomorphisms

An orientation-preserving, recurrent homeomorphism of the two-sphere which is not the identity is shown to admit exactly two fixed points. A recurrent homeomorphism of a compact surface with negative Euler characteristic is periodic.

scholarly journals Recurrence and fixed points of surface homeomorphisms

1988 ◽  
Vol 8 (8) ◽  
pp. 99-107 ◽  
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Lebesgue Measure ◽  
Invariant Chain ◽  
Transitive Set ◽  
Surface Homeomorphisms ◽  
A Chain ◽  
Area Preserving ◽  
Twist Condition

AbstractWe prove that if f is a homeomorphism of the annulus which is homotopic to the identity and has a compact invariant chain transitive set L, then either f has a fixed point or every point of L moves uniformly in one direction: clockwise or counterclockwise. If f is area-preserving, then the annulus itself is a chain transitive set, so, in the presence of a boundary twist condition, one obtains a fixed point. The same techniques apply to homeomorphisms of the torus T2. In this setting we show that if f is homotopic to the identity, preserves Lebesgue measure and has mean translation 0, then it has at least one fixed point.

scholarly journals On non-contractible periodic orbits for surface homeomorphisms

2015 ◽  
Vol 36 (5) ◽  
pp. 1644-1655 ◽  
Author(s):  
FÁBIO ARMANDO TAL
Keyword(s):  
Fixed Points ◽  
Periodic Orbits ◽  
Closed Subset ◽  
Universal Covering ◽  
Periodic Points ◽  
Uniform Bound ◽  
Large Period ◽  
Surface Homeomorphisms ◽  
Rotation Set ◽  
Orientable Surfaces

In this work we study homeomorphisms of closed orientable surfaces homotopic to the identity, focusing on the existence of non-contractible periodic orbits. We show that, if $g$ is such a homeomorphism, and if ${\hat{g}}$ is its lift to the universal covering of $S$ that commutes with the deck transformations, then one of the following three conditions must be satisfied: (1) the set of fixed points for ${\hat{g}}$ projects to a closed subset $F$ which contains an essential continuum; (2) $g$ has non-contractible periodic points of every sufficiently large period; or (3) there exists a uniform bound $M>0$ such that, if $\hat{x}$ projects to a contractible periodic point, then the ${\hat{g}}$ orbit of $\hat{x}$ has diameter less than or equal to $M$. Some consequences for homeomorphisms of surfaces whose rotation set is a singleton are derived.

A Primer on Mapping Class Groups (PMS-49)

2017 ◽  
Author(s):  
Benson Farb ◽  
Dan Margalit
Keyword(s):  
Graduate Students ◽  
Moduli Space ◽  
Riemann Surfaces ◽  
Class Group ◽  
Mapping Class ◽  
Torelli Group ◽  
Surface Bundles ◽  
Surface Homeomorphisms ◽  
Low Dimensional

The study of the mapping class group Mod(S) is a classical topic that is experiencing a renaissance. It lies at the juncture of geometry, topology, and group theory. This book explains as many important theorems, examples, and techniques as possible, quickly and directly, while at the same time giving full details and keeping the text nearly self-contained. The book is suitable for graduate students. It begins by explaining the main group-theoretical properties of Mod(S), from finite generation by Dehn twists and low-dimensional homology to the Dehn–Nielsen–Baer–theorem. Along the way, central objects and tools are introduced, such as the Birman exact sequence, the complex of curves, the braid group, the symplectic representation, and the Torelli group. The book then introduces Teichmüller space and its geometry, and uses the action of Mod(S) on it to prove the Nielsen-Thurston classification of surface homeomorphisms. Topics include the topology of the moduli space of Riemann surfaces, the connection with surface bundles, pseudo-Anosov theory, and Thurston's approach to the classification.

On $\alpha$-nonexpansive mapping and fixed-points in Banach spaces

2018 ◽  
Vol 2018 (-) ◽  
Author(s):  
Prondanai Kaskasem ◽  
Chakkrid Klin-eam ◽  
Suthep Suantai
Keyword(s):  
Nonexpansive Mapping ◽  
Fixed Points ◽  
Banach Spaces

Fixed Points of Sequences of Mappings

2018 ◽  
Vol 2018 (-) ◽  
Author(s):  
C. Ganesa Moorthy ◽  
S. Iruthaya Raj
Keyword(s):  
Fixed Points
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