Table of Contents
ISRN Geometry
Volume 2013, Article ID 379074, 9 pages
http://dx.doi.org/10.1155/2013/379074
Research Article

A Rabbit Hole between Topology and Geometry

CSEM, Flinders University, P.O. Box 2100, Adelaide, SA 5001, Australia

Received 10 July 2013; Accepted 13 August 2013

Academic Editors: A. Ferrandez, J. Keesling, E. Previato, M. Przanowski, and H. J. Van Maldeghem

Copyright © 2013 David G. Glynn. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. S. Lavietes, New York Times obituary, 2003, http://www.nytimes.com/2003/04/07/world/harold-coxeter-96-who-found-profound-beauty-in-geometry.html.
  2. H. S. M. Coxeter, Introduction to Geometry, John Wiley & Sons, New York, NY, USA, 1961. View at MathSciNet
  3. D. G. Glynn, “Theorems of points and planes in three-dimensional projective space,” Journal of the Australian Mathematical Society, vol. 88, no. 1, pp. 75–92, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. P. Dembowski, Finite Geometries, vol. 44 of Ergebnisse der Mathematik und ihrer Grenzgebiete, Springer, New York, NY, USA, 1968. View at MathSciNet
  5. H. F. Baker, Principles of Geometry, vol. 1, Cambridge University Press, London, UK, 2nd edition, 1928.
  6. D. Hilbert, Grundlagen der Geometrie, Göttingen, 1899.
  7. D. G. Glynn, “A note on NK configurations and theorems in projective space,” Bulletin of the Australian Mathematical Society, vol. 76, no. 1, pp. 15–31, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. S. Huggett and I. Moffatt, “Bipartite partial duals and circuits in medial graphs,” Combinatorica, vol. 33, no. 2, pp. 231–252, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  9. L. Heffter, “Ueber das Problem der Nachbargebiete,” Mathematische Annalen, vol. 38, no. 4, pp. 477–508, 1891. View at Publisher · View at Google Scholar · View at MathSciNet
  10. J. R. Edmonds, “A combinatorial representation for polyhedral surfaces,” Notices of the American Mathematical Society, vol. 7, article A646, 1960. View at Google Scholar
  11. B. Bollobás and O. Riordan, “A polynomial invariant of graphs on orientable surfaces,” Proceedings of the London Mathematical Society, vol. 83, no. 3, pp. 513–531, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. B. Bollobás and O. Riordan, “A polynomial of graphs on surfaces,” Mathematische Annalen, vol. 323, no. 1, pp. 81–96, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. G. A. Jones and D. Singerman, “Theory of maps on orientable surfaces,” Proceedings of the London Mathematical Society, vol. 37, no. 2, pp. 273–307, 1978. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. J. Dieudonné, “Les déterminants sur un corps non commutatif,” Bulletin de la Société Mathématique de France, vol. 71, pp. 27–45, 1943. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. I. Gelfand, S. Gelfand, V. Retakh, and R. L. Wilson, “Quasideterminants,” Advances in Mathematics, vol. 193, no. 1, pp. 56–141, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  16. W. Blaschke, Projektive Geometrie, Birkhäuser, Basel, Switzerland, 3rd edition, 1954. View at MathSciNet
  17. H. S. M. Coxeter, “Self-dual configurations and regular graphs,” Bulletin of the American Mathematical Society, vol. 56, pp. 413–455, 1950. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  18. G. Gallucci, Complementi di geometria proiettiva. Contributo alla geometria del tetraedro ed allo studio delle configurazioni, Università degli Studi di Napoli, Napoli, Italy, 1928.
  19. A. F. Moebius, “Kann von zwei dreiseitigen Pyramiden eine jede in Bezug auf die andere um- und eingeschrieben zugleich heissen?” Crelle's Journal für die reine und angewandte Mathematik, vol. 3, pp. 273–278, 1828. View at Google Scholar
  20. A. F. Moebius, “Kann von zwei dreiseitigen Pyramiden eine jede in Bezug auf die andere um- und eingeschrieben zugleich heissen?” Gesammelte Werke, vol. 1, pp. 439–446, 1886. View at Google Scholar
  21. D. G. Glynn, “A slant on the twisted determinants theorem,” Submitted to Bulletin of the Institute of Combinatorics and Its Applications.