Alev MERAL

Dynnikov coordinates on punctured torus

ISSN: 1300-0098
Yayın Aralığı: 6
Yayıncı: TÜBİTAK

We generalize the Dynnikov coordinate system previously defined on the standard punctured disk to anorientable surface of genus-1 with n punctures and one boundary component.

PDF

___

[1] Bestvina M, Handel M. Train-tracks for surface homeomorphisms. Topology 1995; 34 (1): 109-140.
[2] Dehornoy P. Efficient solutions to the braid isotopy problem. Discrete Applied Mathematics 2008; 156 (16): 3091- 3112.
[3] Dehornoy P, Dynnikov I, Rolfsen D, Wiest B. Ordering Braids. Providence, RI, USA: American Mathematical Society, 2008.
[4] Dynnikov I. On a Yang-Baxter map and the Dehornoy ordering. Russian Mathematical Surveys 2002; 57 (3): 592-594.
[5] Haas A, Susskind P. The connectivity of multicurves determined by integral weight train tracks. Transactions of the American Mathematical Society 1992; 329 (2): 637-652.
[6] Hamidi-Tehrani H, Chen Z. Surface diffeomorphisms via train-tracks. Topology and its Applications 1996; 73 (2): 141-167.
[7] Moussafir J. On computing the entropy of braids. Functional Analysis and Other Mathematics 2006; 1 (1): 37-46.
[8] Penner RC, Harer JL. Combinatorics of Train Tracks. Annals of Mathematics Studies. Princeton, NJ: Princeton University Press, 1992.
[9] Yurttaş SÖ, Hall T. On the topological entropy of families of braids. Topology and its Applications 2009; 158 (8): 1554-1564.
[10] Yurttaş SÖ. Geometric intersection of curves on punctured disks. Journal of the Mathematical Society of Japan 2013; 65 (4): 1554-1564.
[11] Yurttaş SÖ, Hall T. Intersections of multicurves from Dynnikov coordinates. Bulletin of Australian Mathematical Society 2018; 98 (1): 149-158.