| Title:
|
Maps on surfaces and Galois groups (English) |
| Author:
|
Jones, Gareth A. |
| Language:
|
English |
| Journal:
|
Mathematica Slovaca |
| ISSN:
|
0139-9918 |
| Volume:
|
47 |
| Issue:
|
1 |
| Year:
|
1997 |
| Pages:
|
1-33 |
| . |
| Category:
|
math |
| . |
| MSC:
|
05C10 |
| idZBL:
|
Zbl 0958.05036 |
| idMR:
|
MR1476746 |
| . |
| Date available:
|
2009-09-25T11:20:00Z |
| Last updated:
|
2012-08-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/136695 |
| . |
| Reference:
|
[1] AHLFORS L. V.: Complex Analysis.McGraw-Hill, Tokyo, 1966. Zbl 0154.31904, MR 0510197 |
| Reference:
|
[2] BELYI G. V.: On Galois extensions of a maximal cyclotomic field.Izv. Akad. Nauk SSSR 43 (1979), 269-276 (Russian) [Math. USSR Izvestiya 14 (1980), 247-256 (English translation)]. Zbl 0409.12012, MR 0534593 |
| Reference:
|
[3] BÉTRÉMA J.-PÉRÉ D.-ZVONKIN A.: Plane trees and their Shabat polynomials.Preprint, Bordeaux, 1992. |
| Reference:
|
[4] BRYANT R. P.-SINGERMAN D.: Foundations of the theory of maps on surfaces with boundary.Quaгt. J. Math. Oxford Ser. (2) 36 (1985), 17-41. Zbl 0565.05026, MR 0780347 |
| Reference:
|
[5] BIGGS N. L.-WHITE A. T.: Permutation Groups and Combinatorial Structures.London Math. Soc. Lecture Note Ser. 33, Cambridge Univ. Press, Cambridge, 1979. Zbl 0415.05002, MR 0540889 |
| Reference:
|
[6] CORI R.: Un code pour les graphes planaires et ses applications.Astéгisque 27 (1975). Zbl 0313.05115, MR 0404045 |
| Reference:
|
[7] CORI R.-MACHI A.: Maps, hypermaps and their automorphisms: a survey I, II, III, Exposition.Math. 10 (1992), 403-427, 429-447, 449-467. MR 1190182 |
| Reference:
|
[8] COUVEIGNES J.-M.: Calcul et rationalité de fonctions de Belyi en genre 0.Ann. Inst. Fourier (Grenoble) 44 (1994). Zbl 0791.11059, MR 1262878 |
| Reference:
|
[9] COX D.: Introduction to Fermaťs Last Theorem.Amer. Math. Monthly 101 (1994), 3-14. MR 1252700 |
| Reference:
|
[10] COXETER H. S. M.-MOSER W. O. J.: Generators and Relations for Discrete Groups.Springer-Verlag, Berlin-Göttingen-Heidelbeгg-New York, 1965. Zbl 0133.28002, MR 0174618 |
| Reference:
|
[11] DOUADY R.-DOUADY A.: Algebre et Théories Galoisiennes II.CEDIC/Fernand Nathan, Paris, 1979. MR 0595328 |
| Reference:
|
[12] GROTHENDIECK A.: Esquisse ďun programme.Preprint, Montpellier, 1984. MR 0556075 |
| Reference:
|
[13] HAMILTON W. R.: Letter to John T. Graves 'On the Icosian' (17th October 1856).In: Mathematical Papers, Vol. III, Algebra (H. Halberstam, R. E. Ingram, eds.), Cambridge University Press, Cambridge, 1967, pp. 612-625. |
| Reference:
|
[14] HEFFTER L.: Über das Problem der Nachbargebiete.Math. Ann. 38 (1891), 477-508. MR 1510685 |
| Reference:
|
[15] HEFFTER L.: Über metacyklische Gruppen und Nachbarconfigurationen.Math. Ann. 50 (1898), 261-268. MR 1510996 |
| Reference:
|
[16] JACOBSON N.: Basic Algebra I, II.Freeman, San Fransisco, 1974, 1980. MR 0356989 |
| Reference:
|
[17] JONES G. A.: Graph imbeddings, groups, and Riemann surfaces.In: Algebraic Methods in Graph Theory, Szeged 1978 (L. Lovasz, V. T. Sos, eds.), North-Holland, Amsterdam, 1981, pp. 397-311. MR 0642049 |
| Reference:
|
[18] JONES G. A.: Congruence and non-congruence subgroups of the modular group.In: Groups, St. Andrews 1985 (E. F. Robertson, C M. Campbell, eds.), London Math. Soc. Lecture Note Ser. 121, Cambridge Univ. Press, Cambridge, 1986, pp. 223-234. MR 0896515 |
| Reference:
|
[19] JONES G. A.-SINGERMAN D.: Theory of maps on orientable surfaces.Proc. London Math. Soc. 37 (1978), 273-307. Zbl 0391.05024, MR 0505721 |
| Reference:
|
[20] JONES G. A.-SINGERMAN D.: Complex Functions, an Algebraic and Geometric Viewpoint.Cambridge University Press, Cambridge, 1987. Zbl 0608.30001, MR 0890746 |
| Reference:
|
[21] JONES G. A.-SINGERMAN D.: Maps, hypermaps and triangle groups.In: The Grothendieck Theory of Dessins d'Enfants (L. Schneps, ed.), London Math. Soc. Lecture Note Ser. 200, Cambridge Univ. Press, Cambridge, 1994, pp. 115-145. Zbl 0833.20045, MR 1305395 |
| Reference:
|
[22] JONES G. A.-SINGERMAN D.: Belyi functions, hypermaps and Galois groups.Bull. London Math. Soc. (To appear). Zbl 0853.14017, MR 1405488 |
| Reference:
|
[23] JONES G. A.-STREIT M.-ZVONKIN A.: Plane trees and Galois groups.Preprint, Southampton, 1994. |
| Reference:
|
[24] MALGOIRE J.-VOISIN C.: Cartes cellulaires.Cahiers Math. Montpellier 12 (1977). Zbl 0405.57003, MR 0515642 |
| Reference:
|
[25] MALLE G.-SAXL J.-WEIGEL T.: Generators of classical groups.Geom. Dedicata 49 (1994), 85-116. MR 1261575 |
| Reference:
|
[26] MATZAT B. H.: Konstruktive Galoistheorie.Lecture Notes in Math. 1284, Springer-Verlag, Berlin, 1987. Zbl 0634.12011, MR 1004467 |
| Reference:
|
[27] MAZUR B.: Number theory as gadfly.Amer. Math. Monthly 98 (1991), 593-610. Zbl 0764.11021, MR 1121312 |
| Reference:
|
[28] REYSSAT E.: Quelques Aspects des Surfaces de Riemann.Birkhaüser, Boston-Basel-Berlin, 1989. Zbl 0689.30001, MR 1034955 |
| Reference:
|
[29] RIBET K. A.: Wiles proves Taniyama's conjecture; Fermat's Last Theorem follows.Notices Amer. Math. Soc. 40 (1993), 575-576. Zbl 1194.11064, MR 1228162 |
| Reference:
|
[30] SCHNEPS L.: Dessins d'enfants on the Riemann sphere.In: The Grothendieck Theory of Dessins d'Enfants (L. Schneps, ed.), London Math. Soc. Lecture Note Ser. 200, Cambridge Univ. Press, Cambridge, 1994, pp. 47-77. Zbl 0823.14017, MR 1305393 |
| Reference:
|
[31]
: The Grothendieck Theory of Dessins d'Enfants.(L. Schneps, ed.), London Math. Soc. Lecture Note Ser. 200, Cambridge University Press, Cambridge, 1994. Zbl 0798.00001, MR 1305390 |
| Reference:
|
[32] SERRE J.-P.: Topics in Galois Theory.Jones and Bartlett, Boston-London, 1992. Zbl 0746.12001, MR 1162313 |
| Reference:
|
[33] SHABAT G. B.-VOEVODSKY V. A.: Drawing curves over number fields.In: Grothendieck Festschrift III (P. Cartier et al., eds.), Progr. Math. 88, Birkhauser, Basel, 1990, pp. 199-227. Zbl 0790.14026, MR 1106916 |
| Reference:
|
[34] SHABAT G.-ZVONKIN A.: Plane trees and algebraic numbers.Preprint, Moscow and Bordeaux, 1993. MR 1310587 |
| Reference:
|
[35] SHAFAREVICH I. R.: Construction of fields of algebraic numbers with given solvable Galois group.Izv. Akad. Nauk. SSSR 18 (1954), 525-578 (Russian) [Amer. Math. Transl. 4 (1956), 185-237 (English translation)]. MR 0071469 |
| Reference:
|
[36] SINGERMAN D.: Automorphisms of maps, permutation groups and Riemann surfaces.Bull. London Math. Soc. 8 (1976), 65-68. Zbl 0322.20001, MR 0393209 |
| Reference:
|
[37] SINGERMAN D.: Universal tessellations.Revista Mat. Univ. Complut. Madrid 1 (1988), 111-123. Zbl 0658.57004, MR 0977044 |
| Reference:
|
[38] TUTTE W. T.: What is a map?.In: New Directions in Graph Theory (F. Harary, ed.), Academic Press, New York, 1973. Zbl 0258.05105, MR 0376413 |
| Reference:
|
[39] VINCE A.: Combinatorial maps.J. Combin. Theory Ser. B 34 (1983), 1-21. Zbl 0514.05032, MR 0701167 |
| Reference:
|
[40] WALSH T. R. S.: Hypermaps versus bipartite maps.J. Combin. Theory Ser. B 18 (1975), 155-163. Zbl 0302.05101, MR 0360328 |
| Reference:
|
[41] WEIL A.: The field of definition of a variety.Amer. J. Math. 78 (1956), 509-524. Zbl 0072.16001, MR 0082726 |
| Reference:
|
[42] WHITE A. T.: Graphs, Groups and Surfaces.North-Holland, Amsterdam, 1973. Zbl 0268.05102 |
| Reference:
|
[43] WOLFART J.: Mirror-invariant triangulations of Riemann surfaces, triangle groups and Grothendieck dessins: variations on a theme of Belyi.Preprint, Frankfurt, 1992. |
| . |
