Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

ON A FAMILY OF BALANCED GROUPS

  • Published : 2007.11.30
Download PDF
⟨ Previous Next ⟩

Abstract

A family of balanced groups is introduced. We describe some geometric approach to find these groups in terms of the (orientable) closed 3-manifolds and its fundamental groups.

Keywords

References

  1. A. Cavicchioli, F. Spaggiari, and M.-O.Wang, A topological study of some groups arising from cellular quotients, Algebra Colloquium 13 (2006), no. 2, 349-380 https://doi.org/10.1142/S1005386706000307
  2. D. J. Collins and H. Zieschang, Combinatorial group theory and fundamental groups, Encyclopaedia Math. Sci. 58, Springer, Berlin, 1993
  3. W. Dunbar, Geometric orbifolds, Rev. Mat. Univ. Complut. Madrid 1 (1998), 67-99
  4. F. Grunewald and U. Hirsch, Link complements arising from arithmetic group actions, Internat. J. Math. 6 (1995), no. 3, 337-370 https://doi.org/10.1142/S0129167X95000109
  5. H. Helling, A. C. Kim, and J. L. Mennicke, A geometric study of Fibonacci groups, J. Lie Theory 8 (1998), no. 1, 1-23
  6. H. M. Hilden, M. T. Lozano, and J. M. Montesinos-Amilibia, The arithmetic of the figure eight knot orbifolds, ToIopology'90 (Eds, B. Apanasov, W. D. Neumann, A. W. Reid, L. Siebenmann), Ohio State Univ., Math. Research Inst. Publ., Walter de Gruyter, Berlin (1992), 169-183
  7. D. F. Holt and W. Plesken, A combinatorial criterion for a finitely presented group to be infinite, J. London Math. Soc. 64 (1968), 603-613
  8. J. M. Montesinos, Classical tessellations and three-manifolds, Springer-Verlag, Berlin- Heidelberg- New York, 1998
  9. L. Neuwirth, An algorithm for the construction of 3-manifolds from 2-complexes, Proc. Cambridge Philos. Soc. 64 (1968), 603-613
  10. H. Seifert and W. Threlfall, A Textbook of Topology, Pure and Applied Mathematics, 89. Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London, 1980
  11. J. R. Stallings, On the recursiveness of sets of presentations of 3-manifold group, Fund. Math. 51 (1962/63), 191-194
  12. M.-O. Wang, A family of complexes with group presentations, Algebra Colloquium 13 (2006), to appear

Cited by

  1. Notes on More Fibonacci Groups vol.15, pp.04, 2008, https://doi.org/10.1142/S1005386708000667