Abstract
Surface laminations are classic closed sets of disjoint curves in surfaces. We give here a full description of how to obtain codings of such laminations when they are non-orientable by using lamination languages, i.e. specific linear complexity languages of two-way infinite words. We also compare lamination languages with symbolic laminations, i.e. the coding counterparts of algebraic laminations.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Belov, A.Y., Chernyatiev, A.L.: Describing the set of words generated by interval exchange transformation. Comm. Algebra 38(7), 2588–2605 (2010)
Berthé, V., Delecroix, V., Dolce, F., Perrin, D., Reutenauer, C., Rindone, G.: Natural coding of linear involutions (2014), arXiv:1405.3529 (see also the abstracts of the 15th Mons Theoretical Computer Science Days)
Birman, J., Series, C.: Geodesics with bounded intersection number on surfaces are sparsely distributed. Topology 24(2), 217–225 (1985)
Bonahon, F.: Geodesic laminations on surfaces. In: Laminations and foliations in dynamics, geometry and topology, Contemp. Math., vol. 269, pp. 1–37. Amer. Math. Soc. (2001)
Cassaigne, J., Nicolas, F.: Factor complexity. In: Combinatorics, automata and number theory, Encyclopedia Math. Appl., vol. 135, pp. 163–247. Cambridge Unversity Press, Cambridge (2010)
Casson, A., Bleiler, S.: Automorphisms of surfaces after Nielsen and Thurston, London Mathematical Society Student Texts, vol. 9. Cambridge Unversity Press, Cambridge (1988)
Cornfeld, I.P., Fomin, S.V., Sinaĭ, Y.G.: Ergodic theory, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 245. Springer, New York (1982)
Coulbois, T., Hilion, A., Lustig, M.: R-trees and laminations for free groups I: Algebraic laminations. J. Lond. Math. Soc. 78(2), 723–736 (2008)
Danthony, C., Nogueira, A.: Measured foliations on nonorientable surfaces. Ann. Sci. École Norm. Sup. (4) 23(3), 469–494 (1990)
Ferenczi, S., Zamboni, L.Q.: Languages of \(k\)-interval exchange transformations. Bull. Lond. Math. Soc. 40(4), 705–714 (2008)
Gadre, V.S.: Dynamics of non-classical interval exchanges. Ergodic Theory Dynam. Systems 32(6), 1930–1971 (2012)
Lando, S.K., Zvonkin, A.K.: Graphs on surfaces and their applications, Encyclopaedia of Mathematical Sciences, vol. 141. Springer, Berlin (2004)
Lee, J.M.: Introduction to smooth manifolds, Graduate Texts in Mathematics, vol. 218, 2nd edn. Springer, New York (2013)
Lopez, L.M., Narbel, P.: Lamination languages. Ergodic Theory Dynam. Systems 33(6), 1813–1863 (2013)
Narbel, P.: Bouquets of circles for lamination languages and complexities. RAIRO, Theoretical Informatics and Applications 48(4), 391–418 (2014)
Penner, R., Harer, J.: Combinatorics of train tracks, Annals of Mathematics Studies, vol. 125. Princeton University Press, Princeton (1992)
Spanier, E.H.: Algebraic topology. Springer, New York (1981)
Thurston, W.: The geometry and topology of three-manifolds (Princeton University Lecture Notes) (Electronic version 1.1 - March 2002). http://library.msri.org/books/gt3m (1980) (accessed September 2014)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this paper
Cite this paper
Lopez, LM., Narbel, P. (2015). Coding Non-orientable Laminations. In: Dediu, AH., Formenti, E., Martín-Vide, C., Truthe, B. (eds) Language and Automata Theory and Applications. LATA 2015. Lecture Notes in Computer Science(), vol 8977. Springer, Cham. https://doi.org/10.1007/978-3-319-15579-1_26
Download citation
DOI: https://doi.org/10.1007/978-3-319-15579-1_26
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-15578-4
Online ISBN: 978-3-319-15579-1
eBook Packages: Computer ScienceComputer Science (R0)