Determining Thurston classes using Nielsen types
نویسندگان
چکیده
منابع مشابه
The Nielsen-Thurston Classification Theorem
Overview: The Nielsen-Thurston Classification Theorem asserts that every element of MCG(Sg) (g ≥ 2) exhibits one of three types of simple behavior. It either has finite order, fixes a nonempty set of of isotopy classes of essential, simple closed curves (reducible), or stretches along a pair of transverse measured foliations in an area-preserving way (pseduo-Anosov). Bers’ strategy for proving ...
متن کاملThe Nielsen-thurston Classification of Mapping Classes Is Determined by Tqft
For each fixed n ≥ 2 we show how the Nielsen-Thurston classification of mapping classes for a closed surface of genus g ≥ 2 is determined by the sequence of quantum SU(n)-representations (ρk)k∈N. That this is the case is a consequence of the asymptotic faithfulness property proved in [A3]. We here provide explicit conditions on (ρk(φ))k∈N, which determines the NielsenThurston type of any mappin...
متن کاملAn Effective Algebraic Detection of the Nielsen–thurston Classification of Mapping Classes
In this article, we propose two algorithms for determining the Nielsen-Thurston classification of a mapping class ψ on a surface S. We start with a finite generating set X for the mapping class group and a word ψ in 〈X〉. We show that if ψ represents a reducible mapping class in Mod(S) then ψ admits a canonical reduction system whose total length is exponential in the word length of ψ. We use th...
متن کاملNielsen-thurston Orderings and the Space of Braid Orderings
We study the topological space of left-orderings of the braid group, and its subspace of Nielsen-Thurston orderings. Our main result is that no Nielsen-Thurston ordering is isolated in the space of braid orderings. In the course of the proof, we classify the convex subgroups and calculate the Conradian soul for any Nielsen-Thurston ordering of Bn. We also prove that for a large class of Nielsen...
متن کاملAsymptotic Linearity of the Mapping Class Group and a Homological Version of the Nielsen–thurston Classification
We study the action of the mapping class group on the integral homology of finite covers of a topological surface. We use the homological representation of the mapping class to construct a faithful infinite–dimensional representation of the mapping class group. We show that this representation detects the Nielsen–Thurston classification of each mapping class. We then discuss some examples that ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1982
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-1982-0662059-x