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RELAXING MULTICURVES ON THE TWICE PUNCTURED MÖBIUS BAND

Yıl 2023, , 16 - 22, 26.06.2023
https://doi.org/10.51477/mejs.1286503

Öz

Let N1,n (n ≥ 1) be a non-orientable surface of genus 1 with n punctures and one boundary component. Generalized Dynnikov coordinates provide a bijection between the set of multicurves in N1,n and Z2n−1 \ {0}. In this paper we restrict to the case where n = 2 and describe an algorithm to relax a multicurve in N1,2 making use of its generalized Dynnikov coordinates

Kaynakça

  • Artin, E., “Theorie der Zöpfe”, Abh. Math. Sem., Univ. Hamburg, 4, 47–72, 1925.
  • Artin, E., “Theory of braids”, Ann. of Math., 48(2), 101–126, 1947.
  • Dynnikov, I., “On a Yang-Baxter mapping and the Dehornoy ordering”, Uspekhi Mat. Nauk, 57(3(345)), 151–152, 2002.
  • Dehornoy, P., Dynnikov, I., Rolfsen, D., and Wiest, B., Ordering braids, Mathematical Surveys and Monographs, vol. 148, American Mathematical Society, Providence, RI, 2008.
  • Hall, T., Yurttaş, S. Ö., “On the topological entropy of families of braids”, Topology Appl., 156(8), 1554–1564, 2009.
  • Hall, T., Yurttaş, S. Ö., “Intersections of multicurves from Dynnikov coordinates”, Bulletin of the Australian Mathematical Society, 98(1), 149–158, 2018.
  • Korkmaz, M., “Mapping class groups of nonorientable surfaces”, Geom. Dedicata 89, 109-133, 2002.
  • Moussafir, J.O., “On computing the entropy of braids”, Funct. Anal. Other Math., 1(1), 37-46, 2006.
  • Yurttaş, S. Ö., Pamuk, M., “Integral laminations on non-orientable surfaces”, Turkish Journal of Mathematics, 42, 69-82, 2018.
  • Yurttaş, S. Ö., “Curves on non-orientable surfaces and crosscap transpositions”, Mathematics, 10(9), 1–33, 2022.
Yıl 2023, , 16 - 22, 26.06.2023
https://doi.org/10.51477/mejs.1286503

Öz

Kaynakça

  • Artin, E., “Theorie der Zöpfe”, Abh. Math. Sem., Univ. Hamburg, 4, 47–72, 1925.
  • Artin, E., “Theory of braids”, Ann. of Math., 48(2), 101–126, 1947.
  • Dynnikov, I., “On a Yang-Baxter mapping and the Dehornoy ordering”, Uspekhi Mat. Nauk, 57(3(345)), 151–152, 2002.
  • Dehornoy, P., Dynnikov, I., Rolfsen, D., and Wiest, B., Ordering braids, Mathematical Surveys and Monographs, vol. 148, American Mathematical Society, Providence, RI, 2008.
  • Hall, T., Yurttaş, S. Ö., “On the topological entropy of families of braids”, Topology Appl., 156(8), 1554–1564, 2009.
  • Hall, T., Yurttaş, S. Ö., “Intersections of multicurves from Dynnikov coordinates”, Bulletin of the Australian Mathematical Society, 98(1), 149–158, 2018.
  • Korkmaz, M., “Mapping class groups of nonorientable surfaces”, Geom. Dedicata 89, 109-133, 2002.
  • Moussafir, J.O., “On computing the entropy of braids”, Funct. Anal. Other Math., 1(1), 37-46, 2006.
  • Yurttaş, S. Ö., Pamuk, M., “Integral laminations on non-orientable surfaces”, Turkish Journal of Mathematics, 42, 69-82, 2018.
  • Yurttaş, S. Ö., “Curves on non-orientable surfaces and crosscap transpositions”, Mathematics, 10(9), 1–33, 2022.
Toplam 10 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Uygulamalı Matematik
Bölüm Makale
Yazarlar

Abdullah Baykal 0000-0001-8011-024X

Ferihe Atalan Bu kişi benim 0000-0001-6547-0570

Saadet Öykü Yurttaş Bu kişi benim 0000-0002-0262-1914

Yayımlanma Tarihi 26 Haziran 2023
Gönderilme Tarihi 1 Mayıs 2023
Kabul Tarihi 19 Haziran 2023
Yayımlandığı Sayı Yıl 2023

Kaynak Göster

IEEE A. Baykal, F. Atalan, ve S. Ö. Yurttaş, “RELAXING MULTICURVES ON THE TWICE PUNCTURED MÖBIUS BAND”, MEJS, c. 9, sy. 1, ss. 16–22, 2023, doi: 10.51477/mejs.1286503.

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This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License

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