DOI QR코드

DOI QR Code

곡면의 tessellation과 regular maps

  • 발행 : 2003.01.01

초록

본 요약논문에서는 단순 연결된 리만곡면들의 isometry군, 그 군의 이산부분군을 이용한 리 만곡면들의 tessellation 그리고 regular map에 대해 소개하고 그 응용과 상호연관성들에 대해 살펴본다. 그리고, 여러가지 관점에서의 regular map의 분류에 대해 소개하고, 최근까지 연구되어진 바에 대해 정리해 보고자 한다.

키워드

참고문헌

  1. Groups and Symmetrys M. A. Armstrong
  2. Rend. Mat. v.4 no.6 Classification of complete maps on orientable surfaces N. L. Biggs
  3. Amer. J. Math. v.48 Regular maps and their groups H. R. Brahana
  4. J. Chem. Inf. Comput. Sci. v.40 no.3 Lists of Face-Regular Polyhedra G. Brinkmann;M. Deza
  5. Determination of all regular maps of small genus M. Conder;P. Dobcsanyi
  6. Geom. Dedicata v.56 Regular maps on non-orientable surfaces M. Conder;B. Everitt https://doi.org/10.1007/BF01267644
  7. Expositiones Math. v.10 Maps, hypermaps and their automorphisms: a survey I, II, III R. Cori;A. Machi
  8. em Generators and Relations for Discrete Groups H. S. M. Coxeter;W. O. J. Moser;Fourth(ed.)
  9. J. Chem. Inf. Comput. Sci. v.40 no.3 Fullerences as Tilings of Surfaces M. Deza;P. W. Fowler;A. Rassat;K. M. Pogers https://doi.org/10.1021/ci990066h
  10. Discrete Math v.64 Enumerating regular objects with a given automorphism group M. L. N. Downs;G. A. Jones
  11. Regular embeddings of complete multipartite graphs S. F. Du;J. H. Kwak;R. Nedela
  12. A classification of regular embeddings of graphs of order a product of two primes S. F. Du;J. H. Kwak;R. Nedela
  13. J. Reine Angew. Math. v.237 Uber die regularen Zerlegungen orientierbarer Flachen D. Garbe
  14. J. London Math. Soc. v.59 Characterization of graphs which underlie regular maps on closed surfaces A. Gardiner;R. Nedela;J. Siran;M. Skoviera https://doi.org/10.1112/S0024610798006851
  15. Math. Ann. v.50 Uber metacyklische Gruppen und Nachbarconfigurationen L. Heffter https://doi.org/10.1007/BF01448067
  16. J. Combin. Theory Ser. v.B39 Regular orientable imbeddings of complete graphs L. D. James;G. A. Jones https://doi.org/10.1016/0095-8956(85)90060-7
  17. Proc. London Math. Soc. v.37 no.3 Theory of maps on orientable surfaces G. A. Jones;D. Singerman https://doi.org/10.1112/plms/s3-37.2.273
  18. Bull. London Math. Soc. v.28 Belyi functions, hypermaps and Galois groups G. A. Jones;D. Singerman https://doi.org/10.1112/blms/28.6.561
  19. Math. Slovaca v.47 Maps on surfaces and Galois groups G. A. Jones
  20. Regular orientable embeddings of complete bipartite graphs J. H. Kwak;Y. S. Kwon
  21. Exponent and switch exponent groups of regular orientable embeddings of complete bipartite graphs J. H. Kwak;Y. S. Kwon
  22. Discrete Comput. Geom. v.11 Residual finiteness of surface groups via tesselations M. L. Lopez https://doi.org/10.1007/BF02574004
  23. Proc. Sympos. Pure Math. v.XII Generators of linear fractional groups A. M. MacBeath
  24. J. London Math. Soc. v.44 A bound for the number of automorphisms of a compact Riemann surface C. MacLachlan https://doi.org/10.1112/jlms/s1-44.1.265
  25. Classical Tessellations and Three-Manifolds J. M. Montesinos
  26. J. Korean Math. Soc. v.38 no.5 Regular Maps-Combinatorial Objects Relating Different Fields of Mathematics R. Nedela
  27. J. Combin. Theory Ser. B v.67 Regular maps of canonical double coverings of graphs R. Nedela;M. Skoviera https://doi.org/10.1006/jctb.1996.0044
  28. Proc. London Math. Soc. v.75 no.3 Exponents of orientable maps R. Nedela;M. Skoviera https://doi.org/10.1112/S0024611597000245
  29. Discrete Math v.238 Four-dimensional football, fullerenes and diagram geometry A. Pasini https://doi.org/10.1016/S0012-365X(00)00414-3
  30. London Math. Soc. Lecture Note Series 200 The Grothendieck Theory of Dessins d'Enfants L. Schneps(ed.)
  31. Proc. London Math. Soc. v.82 no.3 Triangle group representations and constructions of regular maps J. Siran https://doi.org/10.1112/plms/82.3.513
  32. J. Combin. Theory Ser. B v.34 Combinatorial maps A. Vince https://doi.org/10.1016/0095-8956(83)90002-3
  33. J. Combin. Theory Ser. B v.35 Regular combinatorial maps A. Vince https://doi.org/10.1016/0095-8956(83)90053-9
  34. J. Combin. Theory Ser. v.B47 Cantankerous maps and rotary embeddings of $K_n$ S. E. Wilson https://doi.org/10.1016/0095-8956(89)90028-2
  35. Surfaces with no regular hypermaps S. Wilson;A. Breda d'Azevedo