Journal of Mathematical Sciences

, Volume 193, Issue 3, pp 449–460 | Cite as

About “bulky” links generated by generalized Möbius–listing bodies \( GML_2^n \)

  • J. Gielis
  • I. Tavkhelidze
  • P. E. Ricci


In this paper, we consider the “bulky knots” and “bulky links,” which appear after cutting of a Generalized Möbius–Listing \( GML_2^n \) body (with the radial cross section a convex plane 2-symmetric figure with two vertices) along a different Generalized Möbius–Listing surfaces \( GML_2^n \) situated in it. The aim of this report is to investigate the number and geometric structure of the independent objects that appear after such a cutting process of \( GML_2^n \) bodies. In most cases we are able to count the indices of the resulting mathematical objects according to the known classification for the standard knots and links.


Basic Line Cutting Process Radial Cross Section Border Line Convex Plane 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Y. Fougerolle, A. Gribok, S. Foufou, F. Truchetet, and M. A. Abidi, “Radial supershapes for solid modeling,” J. Comput. Sci. Technol., 21, No. 2, 238–243 (2006).CrossRefGoogle Scholar
  2. 2.
    J. Gielis, “A generic geometric transformation that unifies a large range of natural and abstract shapes,” Am. J. Bot., 90, No. 3, 333–338 (2003).CrossRefGoogle Scholar
  3. 3.
    A. Gray, E. Abbena, and S. Salamon, Modern Differential Geometry of Curves and Surfaces with Mathematica ®, Chapman & Hall/CRC, Boca Raton (2006).MATHGoogle Scholar
  4. 4.
    P. E. Ricci and I. Tavkhelidze, “On some geometric characteristic of the generalized Möbius–Listing surfaces,” Georgian Math. J., 18, No.2 (2009).Google Scholar
  5. 5.
    I. Tavkhelidze, “Classification of a wide set of geometric figures,” Lect. Notes TICMI, 8, 53–61 (2007).MathSciNetMATHGoogle Scholar
  6. 6.
    I. Tavkhelidze, “On the connection of the generalized Möbius–Listing surfaces \( GML_m^n \) with sets of ribbon knots and links,” in: Proc. Int. Conf. “Modern Algebra and Its Applications,” September 2026, 2010, Batumi, Georgia, Batumi (2010), pp. 147–152,Google Scholar
  7. 7.
    I. Tavkhelidze, C. Cassisa, and P. E. Ricci, “On the connection of the generalized Möbius–Listing surfaces with sets of knots and links,” in: Lecture Notes of Seminario Interdisciplinare di Matematica, 9 (2010), pp. 73–86.Google Scholar
  8. 7.
    I. Tavkhelidze and P. E. Ricci, “Classification of a wide set of geometric figures, surfaces and lines (trajectories),” Rend. Accad. Naz. Sci. XL Mem. Mat. Appl. (5), 30, 191–212 (2006).MathSciNetGoogle Scholar
  9. 8.
    E. W.Weisstein, CRC Concise Encyclopedia of Mathematics, Chapman & Hall/CRC, Boca Raton (2003).Google Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Department of Bioscience EngineeringGenicap BV & University of AntwerpAntwerpBelgium
  2. 2.Department of MathematicsI. Javakhishvili Tbilisi State UniversityTbilisiGeorgia
  3. 3.Campus Bio-Medico & International TelematicUniversity UniNettunoRomaItaly

Personalised recommendations