On the Infinite Loch Ness monster
John A. Arredondo; Camilo Ramírez Maluendas
Commentationes Mathematicae Universitatis Carolinae (2017)
- Volume: 58, Issue: 4, page 465-479
- ISSN: 0010-2628
Access Full Article
topAbstract
topHow to cite
topArredondo, John A., and Ramírez Maluendas, Camilo. "On the Infinite Loch Ness monster." Commentationes Mathematicae Universitatis Carolinae 58.4 (2017): 465-479. <http://eudml.org/doc/294631>.
@article{Arredondo2017,
abstract = {In this paper we introduce the topological surface called \{Infinite Loch Ness monster\}, discussing how this name has evolved and how it has been historically understood. We give two constructions of this surface, one of them having translation structure and the other hyperbolic structure.},
author = {Arredondo, John A., Ramírez Maluendas, Camilo},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {Infinite Loch Ness monster; tame Infinite Loch Ness monster; hyperbolic Infinite Loch Ness monster},
language = {eng},
number = {4},
pages = {465-479},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On the Infinite Loch Ness monster},
url = {http://eudml.org/doc/294631},
volume = {58},
year = {2017},
}
TY - JOUR
AU - Arredondo, John A.
AU - Ramírez Maluendas, Camilo
TI - On the Infinite Loch Ness monster
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2017
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 58
IS - 4
SP - 465
EP - 479
AB - In this paper we introduce the topological surface called {Infinite Loch Ness monster}, discussing how this name has evolved and how it has been historically understood. We give two constructions of this surface, one of them having translation structure and the other hyperbolic structure.
LA - eng
KW - Infinite Loch Ness monster; tame Infinite Loch Ness monster; hyperbolic Infinite Loch Ness monster
UR - http://eudml.org/doc/294631
ER -
References
top- Abikoff W., The uniformization theorem, Amer. Math. Monthly 88 (1981), no. 8, 574–592. Zbl0482.30034MR0628026
- Arredondo J.A., Ramírez Maluendas C., On infinitely generated Fuchsian groups of some infinite genus surfaces, preliminary manuscript.
- Arredondo J.A., Ramírez Maluendas C., Valdez F., 10.1016/j.disc.2016.12.023, Discrete Math. 340 (2017), no. 6, 1180–1186. Zbl1369.05101MR3624603DOI10.1016/j.disc.2016.12.023
- Beardon A.F., A Premier on Riemann Surfaces, London Mathematical Society Lecture Note Series, 78, Cambridge University Press, Cambridge, 1984. MR1238511
- Cantwell J., Conlon L., Leaf prescriptions for closed -manifolds, Trans. Amer. Math. Soc. 236 (1978), 239–261. Zbl0398.57009MR0645738
- Cantwell J., Conlon L., 10.1016/0040-9383(77)90038-6, Topology 16 (1977), no. 4, 311–322. Zbl0385.57007MR0645739DOI10.1016/0040-9383(77)90038-6
- Conway J.H., Burgiel H., Goodman-Strauss C., The Symmetries of Things, A K Peters, Ltd., Wellesley, Massachusetts, 2008. Zbl1173.00001MR2410150
- Coxeter H.S.M., Regular skew polyhedra in three and four dimension, and their topological analogues, Proc. London Math. Soc. (2) 43 (1937), no. 1, 33–62. MR1575418
- Fox R.H., Kershner R.B., 10.1215/S0012-7094-36-00213-2, Duke Math. J. 2 (1936), no. 1, 147–150. Zbl0014.03401MR1545913DOI10.1215/S0012-7094-36-00213-2
- Ghys É., 10.2307/2118526, Ann. of Math. (2) 141 (1995), no. 2, 387–422. Zbl0843.57026MR1324140DOI10.2307/2118526
- Hilbert D., 10.1090/S0273-0979-00-00881-8, Bull. Amer. Math. Soc. (N.S.) 37 (2000), no. 4, 407–436; reprinted from Bull. Amer. Math. Soc. 8 (1902), 437–479. Zbl0979.01028MR1779412DOI10.1090/S0273-0979-00-00881-8
- Hubert P., Schmidt T.A., An introduction to Veech surfaces, Handbook of dynamical systems, 1B, Elsevier B.V., Amsterdam, 2006, pp. 501–526. Zbl1130.37367MR2186246
- Katok S., Fuchsian Groups, Chicago Lectures in Mathematics, University of Chicago Press, Chicago, IL, 1992. Zbl1243.37029MR1177168
- Katok A.B., Zemljakov A.N., Topological transitivity of billiards in polygons, Mat. Zametki 18 (1975), no. 2, 291–300 (Russian). MR0399423
- Kerckhoff S., Masur H., Smillie J., 10.2307/1971280, Ann. of Math. 124 (1986), no. 2, 293–311. Zbl0637.58010MR0855297DOI10.2307/1971280
- Kerékjártó B., Vorlesungen über Topologie I, Mathematics: Theory & Applications, Springer, Berlin, 1923.
- Kontsevich M., Zorich A., 10.1007/s00222-003-0303-x, Invent. Math. 153 (2003), no. 3, 631–678. MR2000471DOI10.1007/s00222-003-0303-x
- Loxton J.H., Captain Cook and the Loch Ness Monster, James Cook Mathematical Notes 27 (1981), no. 3, 3060–3064.
- Loxton J.H., 10.1112/S0025579300010500, Mathematika 30 (1983), no. 2, 153–163. Zbl0517.10040MR0737174DOI10.1112/S0025579300010500
- Maskit B., Kleinian Groups, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 287, Springer, Berlin, 1988. Zbl0940.30022MR0959135
- Masur H., Tabachnikov S., Rational billiards and flat structures, Handbook of dynamical systems, 1A, North-Holland, Amsterdam, 2002, pp. 1015–1089. Zbl1057.37034MR1928530
- Möller M., 10.1007/s00222-006-0510-3, Invent. Math. 165 (2006), 633–649. Zbl1111.14019MR2242629DOI10.1007/s00222-006-0510-3
- Muciño-Raymundo J., Superficies de Riemann y Uniformización, http://www.matmor.unam.mx/~muciray/articulos/Superficies_de_Riemann.pdf.
- Nishimori T., 10.1093/qmath/26.1.159, Quart. J. Math. 26 (1975), no. 1, 159–167. Zbl0303.57012MR0377927DOI10.1093/qmath/26.1.159
- Phillips A., Sullivan D., 10.1016/0040-9383(81)90039-2, Topology 20 (1981), no. 2, 209–218. Zbl0454.57016MR0605659DOI10.1016/0040-9383(81)90039-2
- Przytycki P., Schmithüsen G., Valdez F., 10.5802/aif.2625, Ann. Inst. Fourier (Grenoble) 61 (2011), no. 2, 673–687. Zbl1266.32016MR2895069DOI10.5802/aif.2625
- Ramírez Maluendas C., Valdez F., 10.2140/agt.2017.17.529, Algebr. Geom. Topol. 17 (2017), no. 1, 529–560. MR3604384DOI10.2140/agt.2017.17.529
- Richards I., 10.1090/S0002-9947-1963-0143186-0, Trans. Amer. Math. Soc. 106 (1963), 259–269. Zbl0156.22203MR0143186DOI10.1090/S0002-9947-1963-0143186-0
- Sondow J., 10.1090/S0002-9904-1975-13764-5, Bull. Amer. Math. Soc. 81 (1975), no. 3, 622–624. Zbl0309.57012MR0365591DOI10.1090/S0002-9904-1975-13764-5
- Specker E., 10.1007/BF02565606, Comment. Math. Helv. 23 (1949), 303–333. Zbl0036.12803MR0033520DOI10.1007/BF02565606
- Spivak M., A comprehensive introduction to differential geometry, Vol. I, second edition, Publish or Perish, Inc., Wilmington, Del., 1979. Zbl0439.53001MR0532834
- Steuart C., The Loch Ness Monster: The Evidence, Prometheus Books, USA, 1997.
- Valdez F., 10.1007/s10711-009-9378-x, Geom. Dedicata 143 (2009), 143–154. Zbl1190.37040MR2576299DOI10.1007/s10711-009-9378-x
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.