Surface diffeomorphisms via train-tracks

Hamidi-Tehrani, Hessam; Zong-He, Chen

doi:10.1016/0166-8641(96)00024-7

Cited by 13 publications

(9 citation statements)

References 5 publications

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“…Bu bölümde train track grafikleri [2,11,12] tanıtılacak, çoklu eğrilerin bu grafiklerle nasıl koordinatlandırıldığı gösterilecektir. Tanım 2.2.…”

Section: Train Track Koordinatlarıunclassified

“…Bölüm)-düşük boyutlu topoloji ve hesaplamalı topolojide merkezi bir rol oynamaktadır. Böyle sistemler genellikle Dehn-Thurston koordinatları veya train track koordinatları tarafından tanımlanmaktadır [14,2,11,12]. Yüzeyin -noktası çıkarılmış diski ( adet işaretlenmiş noktalı disk) olması durumunda çoklu eğrileri tanımlamanın alternatif ve oldukça kullanışlı bir yolu çoklu eğrilerin kümesi ile ℤ 2 −4 \{0} ( ≥ 3) arasında birebir ve örten bir fonksiyon tanımlayan Dynnikov koordinat sistemini kullanmaktır [5,6,13,3,4,10,17,18,19,20].…”

Section: Introductionunclassified

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Dynnikov koordinatları ve π_1–train track grafikleri

Yurttaş

Gungorur

2019

Academic Platform Journal of Engineering and Science

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Verilen bir yüzeyde tanımlı çoklu eğrileri koordinatlandırmanın alışılmış bir yolu train track grafiklerini kullanmaktır. Yüzeyin sonlu noktası çıkarılmış diski olması durumunda ise çoklu eğrilerin kümesi ile ℤ 2 −4 \{0} arasında birebir ve örten bir dönüşüm veren Dynnikov koordinat sistemi çoklu eğrileri koordinatlandırmak için alternatif ve etkili bir yol sunar. Bu çalışmada, ' de verilen bir çoklu eğrinin belirli tipten bir train track grafiği olan 1-train track grafiği koordinatlarını Dynnikov koordinatlarına bağlayan geçiş formülleri sunulmuştur.

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“…Bu bölümde train track grafikleri [2,11,12] tanıtılacak, çoklu eğrilerin bu grafiklerle nasıl koordinatlandırıldığı gösterilecektir. Tanım 2.2.…”

Section: Train Track Koordinatlarıunclassified

Section: Introductionunclassified

Dynnikov koordinatları ve π_1–train track grafikleri

Yurttaş

Gungorur

2019

Academic Platform Journal of Engineering and Science

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“…Algorithmic proofs of Thurston's classification theorem [18,19,5] are given for disk homeomorphisms in [13] and for surface homeomorphisms in [1] and a different algorithm based on piecewise linear actions was described in [7]. Given a free group automorphism induced by a surface homeomorphism, the algorithms explicitly find the invariant train track if the mapping class is pseudo-Anosov, and enable one to calculate among other things the topological entropy of the pseudo-Anosov representative.…”

Section: G] As the Infimum Inf {H(f) \ [F] = [G]}mentioning

confidence: 99%

Entropies of Braids

Song

Los³

2002

J. Knot Theory Ramifications

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Pseudo-Anosov homeomorphisms are classified by their invariant train tracks. The decomposition of any train track map in elementary folding maps gives a normal form for each train track class. In the case of 4-braids there are three train tracks classes and we give an explicit automaton that generates a normal form for each class. This enables us, for instance, to exhibit the pseudo-Anosov 4-braid with the minimal growth rate. We also show that the growth rate of a pseudo-Anosov braid appears as a root of the Alexander polynomial of a link that shares a common sub-link with the closure of the braid. We finally give a criterion for the faithfulness of the Burau representation for 4-braids. 647J. Knot Theory Ramifications 2002.11:647-666. Downloaded from www.worldscientific.com by MICHIGAN STATE UNIVERSITY on 02/03/15. For personal use only. J. Knot Theory Ramifications 2002.11:647-666. Downloaded from www.worldscientific.com by MICHIGAN STATE UNIVERSITY on 02/03/15. For personal use only.

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“…Similar algorithms for the disk case were given in [9,18]. Also, different algorithms were given in [1,11]. Our theorem provides an algebraic approach to this problem.…”

Section: Introductionmentioning

confidence: 96%

The generalized Lefschetz number of homeomorphisms on punctured disks

Matsuoka¹

2009

J. Math. Soc. Japan

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We compute the generalized Lefschetz number of orientation-preserving selfhomeomorphisms of a compact punctured disk, using the fact that homotopy classes of these homeomorphisms can be identified with braids. This result is applied to study Nielsen-Thurston canonical homeomorphisms on a punctured disk. We determine, for a certain class of braids, the rotation number of the corresponding canonical homeomorphisms on the outer boundary circle. As a consequence of this result on the rotation number, it is shown that the canonical homeomorphisms corresponding to some braids are pseudo-Anosov with associated foliations having no interior singularities. 0 2000 Mathematics Subject Classification. Primary 37E30; Secondary 55M20.

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Surface diffeomorphisms via train-tracks

Cited by 13 publications

References 5 publications

Dynnikov koordinatları ve π_1–train track grafikleri

Dynnikov koordinatları ve π_1–train track grafikleri

Entropies of Braids

The generalized Lefschetz number of homeomorphisms on punctured disks

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