Chiral hypermaps with few hyperfaces

Antonio J. Breda d'Azevedo; Roman Nedela

Mathematica Slovaca (2003)

  • Volume: 53, Issue: 2, page 107-128
  • ISSN: 0232-0525

How to cite

top

Breda d'Azevedo, Antonio J., and Nedela, Roman. "Chiral hypermaps with few hyperfaces." Mathematica Slovaca 53.2 (2003): 107-128. <http://eudml.org/doc/31944>.

@article{BredadAzevedo2003,
author = {Breda d'Azevedo, Antonio J., Nedela, Roman},
journal = {Mathematica Slovaca},
keywords = {graph; map; hypermap; group; surface; mirror symmetry; embedding},
language = {eng},
number = {2},
pages = {107-128},
publisher = {Mathematical Institute of the Slovak Academy of Sciences},
title = {Chiral hypermaps with few hyperfaces},
url = {http://eudml.org/doc/31944},
volume = {53},
year = {2003},
}

TY - JOUR
AU - Breda d'Azevedo, Antonio J.
AU - Nedela, Roman
TI - Chiral hypermaps with few hyperfaces
JO - Mathematica Slovaca
PY - 2003
PB - Mathematical Institute of the Slovak Academy of Sciences
VL - 53
IS - 2
SP - 107
EP - 128
LA - eng
KW - graph; map; hypermap; group; surface; mirror symmetry; embedding
UR - http://eudml.org/doc/31944
ER -

References

top
  1. BREDA D'AZEVEDO A., The reflexible hypermaps of characteristic -2, Math. Slovaca 47 (1997), 131-153. (1997) Zbl1053.05504MR1476863
  2. BREDA D'AZEVEDO A., Face-class action, Geometria, Física-Matemática e outros Ensaios, Dep. Mat. Coimbra (1998), 55-67. (1998) 
  3. BREDA D'AZEVEDO A.-JONES G., Double coverings and reflexible abelian hypermaps, Contrib. Algebra Geom. 41 (2000), 371-389. MR1801428
  4. BREDA D'AZEVEDO A.-JONES G., Platonic hypermaps, Beitrage Algebra Geom. 42 (2001), 1-37. Zbl0968.05022MR1824748
  5. BREDA D'AZEVEDO A.-JONES G., Rotary hypermaps of genus 2, Beitrage Algebra Geom. 42 (2001), 39-58. Zbl0968.05023MR1824749
  6. BREDA D'AZEVEDO A.-JONES G.-NEDELA R.-SKOVIERA M., Chirality index of maps and hypermaps, (Submitted). 
  7. BREDA D'AZEVEDO A.-NEDELA R., Chiral hypermaps of small genus, Beitrage Algebra Geom. 44 (2003), 127-143. Zbl1014.05020MR1990988
  8. BRYANT R. P.-SINGERMAN D., Foundations of the theory of maps on surfaces with boundary, Quart. J. Math. Oxford Ser. (2) 36 (1985), 17-41. (1985) Zbl0565.05026MR0780347
  9. BURNSIDE W., Theory of Groups of Finite Order, Cambridge Univ. Press, Cambridge, 1911. (1911) 
  10. CONDER M.-DOBCSANYI P., Determination of all regular maps of small genus, J. Combin. Theory Ser. B 81 (2001), 224-242. Zbl1028.05045MR1814906
  11. CORN D.-SINGERMAN D., Regular hypermaps, European J. Combin. 9 (1988), 337-351. (1988) Zbl0665.57002MR0950053
  12. COXETER H. S. M.-MOSER W. O. J., Generators and Relations for Discrete groups, (3rd ed.), Springer-Verlag, New York, 1972. (1972) Zbl0239.20040MR0349820
  13. ISQUIERDO M.-SINGERMAN D., [unknown], European J. Combin. 2 (1994), 159-172. (1994) 
  14. SCHONERT M., al., GAP - Groups, Algorithms, and Programming, (4th ed.). Lehrstuhl D für Mathematik, Rheinisch Westfalische Technische Hochschule, Aachen (Germany), 1994. (1994) 
  15. GARBE D., Über die reguldren Zerlegungen orientierbarer Flächen, J. Reine Angew. Math. 237 (1969), 39-55. (1969) MR0246198
  16. JONES G., Maps on surfaces and galois groups, , Math. Slovaca 47 (1997), 1-33. (1997) Zbl0958.05036MR1476746
  17. JONES G.-SINGERMAN D., Theory of maps on orientable surfaces, Proc. London Math. Soc. (3) 37 (1978), 273-307. (1978) Zbl0391.05024MR0505721
  18. JONES G.-SINGERMAN D., Belyi functions, hypermaps and Galois groups, Bull. London Math. Soc. 28 (1996), 561-590. (1996) Zbl0853.14017MR1405488
  19. JONES G. A.-SINGERMAN D.-WILSON S., Chiral triangular maps and non-symmetric Riemann surfaces, Preprint. 
  20. JONSON D. L., Topics in the Theory of Group Presentations, London Math. Soc. Lecture Note Ser. 42, Cambridge Univ. Press, Cambridge, 1980. (1980) MR0695161
  21. NEDELA R.-SKOVIERA M., Exponents of orientable maps, Proc. London Math. Soc. (3) 75 (1997), 1-31. (1997) Zbl0877.05012MR1444311
  22. SHERK F. A., The regular maps on a surface of genus three, Canad. J. Math. 11 (1959), 452-480. (1959) Zbl0086.16102MR0107203
  23. VINCE A., Combinatorial maps, J. Combin. Theory Ser. B 34 (1983), 1-21. (1983) Zbl0514.05032MR0701167
  24. WALSH T. R. S., Hypermaps versus bipartite maps, J. Combin. Theory Ser. B 18 (1975), 155-163. (1975) Zbl0302.05101MR0360328
  25. WILSON S.-BREDA D'AZEVEDO A., Surfaces with no regular hypermaps, (Submitted). 

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.