Abstract
Any link in ℝ3 is isotopic to a link lying on the union T of three half-planes with common boundary line. A nontrivial theory of knots and links on T was developed by the same author in an earlier paper. In the present paper, the results obtained are interpreted in the context of M. Gusarov's theory of invariants of finite degree (cubic space theory). Bibliography: 6 titles.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
REFERENCES
M. N. Gusarov (M. Goussarov), “Interdependent modifications of links and invariants of finite degree," U.U.D.M. Report 1995:26.
M. N. Gusarov, “Axiomatic cubic space theory," unpublished.
M. N. Gusarov (M. Goussarov), M. Poliak, and O. Viro, “Finite type invariants of classical and virtual knots," Preprint (1998).
Ka Yi Ng and T. Stanford, “On Gusarov's groups of knots," Preprint (1995).
J.-P. Serre, Lie Algebras and Lie Groups, Benjamin, New York (1965).
P. V. Svetlov, “Invariants of knots and links on T-polyhedra,” Zap. Nauchn. Semin. POMI, 252, 231–246(1998).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Svetlov, P.V. Links on T-Polyhedra: Examples of Gusarov's Cubic Spaces. Journal of Mathematical Sciences 113, 879–886 (2003). https://doi.org/10.1023/A:1021203906238
Issue Date:
DOI: https://doi.org/10.1023/A:1021203906238