Periodic classes 10 2. FAST ALGORITHMIC NIELSEN-THURSTON CLASSIFICATION OF FOUR-STRAND BRAIDS MATTHIEU CALVEZ AND BERT WIEST Abstract. ideal triangulation of N (C) Figures - uploaded by Tsukasa Ishibashi. Cluster-pA classes of special type: cluster Dehn twists 17 3. Fast algorithmic Nielsen-Thurston classification of four-strand braids.
Download PDF: Sorry, we are unable to provide the full text but you may find it at the following location(s): nielsen-thurston classification pdf Thomas Koberda and Johanna Mangahas, An effective algebraic detection of the Nielsen-Thurston classification of mapping classes, J. Basic examples: seeds associated with triangulated surfaces 19 3. Fast Nielsen–Thurston classiﬁcation of braids 1747 The relation 4 on Bn deﬁned by x 4 y if and only if x1y 2BC n deﬁnes a partial order called preﬁx order, which turns out to be a lattice order.
We use the homological representation of the mapping class to construct a faith-ful in nitedimensional representation of the mapping class group. nielsen-thurston classification pdf Nielsen and Thurston proved that any homeomorphism of S can be isotoped to be in one of three standard geometric forms&39;, called Nielsen-Thurston nielsen-thurston classification pdf classification. fr ABSTRACT nielsen-thurston classification pdf We give an algorithm which decides the Nielsen-Thurston type of a given four-strand braid. This theorem induces a natural classification for braids. The proof of its validity is based on a result.
AN EFFECTIVE ALGEBRAIC DETECTION OF THE NIELSENTHURSTON CLASSIFICATION nielsen-thurston classification pdf OF MAPPING CLASSES nielsen-thurston classification pdf THOMAS KOBERDA AND JOHANNA MANGAHAS J Abstract. FAST ALGORITHMIC NIELSEN-THURSTON CLASSIFICATION OF FOUR -STRAND BRAIDS3 in D 4: the rst is round, the second is almost-round and is nielsen-thurston classification pdf sent to a nielsen-thurston classification pdf roun d curve by the permutation braid 1 3, the third is of complexity 2 and is obtained from the rst by applying 2 2. The first is the Nielsen-Thurston classification problem: given a mapping class, determine if it is periodic, reducible, or. We show that this representation detects the Nielsen–Thurston classification of each mapping class. We also prove an effective conjugacy separability result for pi1(S) which allows us to lift the action of ψ to a finite cover S ̃ of S whose degree depends computably on the word length of ψ, and to use pdf the homology action of ψ on H1(S̃,C) to determine the Nielsen-Thurston classification of ψ. 1, 1-21) pdf "Right-angled Artin groups and finite subgraphs of curve complexes. Topics: braids, Nielsen-Thurston classification, algorithm, Garside theory, 20F36, 20F10, MATH.
Topological pdf Quantum Field Theory and the Nielsen-Thurston classification of M(0,4) By Jorgen Ellegaard Andersen, Gregor Masbaum and Kenji Ueno Download PDF (225 nielsen-thurston classification pdf KB). We then discuss some examples. Topics include the topology of the moduli space of Riemann nielsen-thurston classification pdf surfaces, the connection with surface bundles, pseudo-Anosov theory, and Thurston&39;s approach to the classification. We nielsen-thurston classification pdf give an algorithm which decides the Nielsen-Thurston type of a given four-strand braid. From a naive point of view, translation distances in the curve complex should serve the same purpose as translation distances in Teichmuller space.
THE NIELSEN-THURSTON CLASSIFICATION AND AUTOMORPHISMS OF A FREE GROUP II Z. In what follows the. Download pdf, with Thomas Koberda; Journal of Topology and Analysis (). Nielsen-Thurston Theory. Convex cocompactness in nielsen-thurston mapping class groups via quasiconvexity in right-angled Artin groups. A Primer on Mapping Class Groups. 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. First, we’ll outline a nielsen-thurston classification pdf fact about the structure of geodesics laminations.
We show that the Nielsen–Thurston classification of mapping classes of the sphere with four marked points is. William Thurston &39;s theorem completes the work initiated by Jakob Nielsen. The well-known connection between braids and mapping classes on the n-punctured nielsen-thurston disc can be exploited to decide, using braid-theoretic nielsen-thurston classification pdf techniques, the place of a given isotopy class in the Nielsen-Thurston classification as reducible or irreducible, and in the latter case, as periodic or pseudo-Anosov. algorithm for the Nielsen-Thurston Classification Problem.
Nielsen Thurston Classification H If4ENS is not reducible a finiteorder then has a representative fc Homeot s which is fpseudotnosow. In mathematics, Thurston&39;s classification theorem characterizes homeomorphisms of a compact orientable surface. The Nielsen–Thurston Classification (). Analysis, no. The word reducible in nielsen-thurston the context nielsen-thurston classification pdf of the braid groups could be confusing. Deﬁnition of the seed 19 3. A proof of the Nielsen-Thurston classiﬁcation of mapping class elements Sayantan Khan Tuesday 27th August, This proof will follow along the lines of nielsen-thurston classification pdf Mar16, Chapter nielsen-thurston classification pdf 8, but will ﬂesh out some of the details, as well as outlining potential subtleties.
MATH-GR Mathematics math/Group Theory math. pseudo-Anosov — nontrivial stretching. Cluster-reducible nielsen-thurston classes 12 2. The proof of its validity is based on a result which states that for a reducible 4-braid which is as short as possible within its conjugacy class (short in the sense of Garside. In this article, we propose two algorithms nielsen-thurston classification pdf for determining the nielsen-thurston classification pdf Nielsen-Thurston clas-si cation of a mapping class on a surface S.
Nielsen-Thurston Classification Every braid is one of the following: 1. Download PDF Abstract: 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, when one considers all levels. Full text views reflects the number of PDF. We study the action of the mapping class group on the in-tegral homology of nite covers of a topological surface. Sela1;2 We elaborate the techniques of Se1 nielsen-thurston classification pdf to construct a (canonical) hierarchical decompo-sition of a free group with respect to a given automorphism of it.
We give an algorithm which decides the Nielsen–Thurston type of a given four-strand braid. Nielsen-Thurston types on cluster modular groups 10 2. Given nielsen-thurston a homeomorphism f : S → S, there is a map g isotopic to f pdf such that at least one of the following holds:. Our decomposition generalizes the Nielsen-Thurston classi cation for automorphisms of surfaces and,. nielsen-thurston eBook (PDF) ISBN. (a) (b) (c) Figure 1. An effective algebraic detection of the Nielsen-Thurston classification of mapping classes. Fast Nielsen–Thurston classiﬁcation of braids 1747 The relation nielsen-thurston 4 on Bn deﬁned by x 4 y if and only if x1y 2BC n deﬁnes a partial order called preﬁx order, which turns out to be a lattice order.
(To appear in Geom. tl I F a fan of transverse Gingular measuredfoliations Ft F on S Kid at f ft K F. TheNielsenThe Nielsen-ThurstonClassificationThurston Classification. ) pdf "An effective algebraic detection of the Nielsen-Thurston classification of mapping classes. NIELSENTHURSTON CLASSIFICATION THOMAS nielsen-thurston classification pdf KOBERDA Abstract.
It first considers the classification of elements for the torus of Mod(T² before discussing higher-genus analogues for each of the three types of elements of Mod(T². Request PDF | Fast Nielsen–Thurston classification of braids | We prove the nielsen-thurston classification pdf existence of an algorithm which solves the reducibility problem in braid groups nielsen-thurston classification pdf and runs in quadratic time with. Description: Let S be a closed orientable surface of positive genus. We study the action of the mapping class group on the integral homology of finite covers of pdf a nielsen-thurston classification pdf topological surface. I am curious to see if anyone knows a proof of the Nielsen-Thurston classification of mapping classes that does not depend on results in Teichmuller theory.
The complexity of our algorithm is quadratic with respect to word length. Fast Nielsen-Thurston Classification Dan Margalit, Georgia Tech In joint work with Balazs Strenner and Oyku Yurttas, we consider two algorithmic questions concerning the mapping class group. " Joint with Sang-hyun Kim.
That this is the case is a consequence nielsen-thurston classification pdf of our asymptotic faithfulness property. The seed associated with an ideal triangulation is of Teichmu. Fast algorithmic Nielsen-Thurston classiﬁcation of 4-braids Matthieu Calvez, Bert Wiest IRMAR, Université de Rennes 1 Conference on Garside theory, Caen, 30 june. We start with a nite generating set X for the. FAST ALGORITHMIC NIELSEN-THURSTON CLASSIFICATION OF FOUR-STRAND BRAIDS MATTHIEU CALVEZ and BERT WIEST IRMAR, Universit´e de Rennes 1, Campus de Beaulieu 35042 Rennes nielsen-thurston classification pdf Cedex, nielsen-thurston classification pdf France matthieu. " Joint with Johanna Mangahas. We give an algorithm which decides the Nielsen-Thurston type of a given four-strand braid.
classified by the Nielsen-Thurston theorem 21,23 into three dynamical typesperiodic, pseudo-,4nosov and reducible. Topological quantum field theory nielsen-thurston classification pdf and the Nielsen-Thurston nielsen-thurston classification pdf classification of M(0,4). We use the homological representation of the mapping class to construct a faithful infinite-dimensional representation pdf of the mapping class group. We will denote by ˝the inner automorphism associated nielsen-thurston to †: this is an involution which for each i maps ˙i. The nielsen-thurston classification pdf characterization gives an analogue of the Nielsen-Thurston classification theory on the mapping class group of a surface. This chapter explains and proves the Nielsen–Thurston classification of elements of Mod(S), one of the central theorems in the study of mapping class groups.
Joint with Sang-hyun Kim.
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