1. Algebraic and topological structures on rational tangles
- Author
-
Seyed M.H. Mansourbeigi, Vida Milani, Hossein Finizadeh, and Poli Paper
- Subjects
tangle convergent ,Coalgebra ,Structure (category theory) ,Bi-pseudo-module ,010103 numerical & computational mathematics ,Interval (mathematics) ,lcsh:Analysis ,Group Hopf algebra ,Continued fraction ,Topology ,01 natural sciences ,Tangle ,Interval coalgebra ,Incidence algebra ,Mathematics::Quantum Algebra ,Physical Sciences and Mathematics ,Order (group theory) ,0101 mathematics ,Algebraic number ,Mathematics ,group Hopf algebra ,Computer Sciences ,lcsh:Mathematics ,lcsh:QA299.6-433 ,Tangle convergen ,bi-pseudo-module ,lcsh:QA1-939 ,Mathematics::Geometric Topology ,continued fraction ,010101 applied mathematics ,Algebra ,incidence algebra ,pseudo-tensor product ,Pseudo-tensor product ,Pseudo-module ,pseudo-module ,Geometry and Topology ,tangle ,Locally finite partial order ,locally finite partial order ,interval coalgebra - Abstract
In this paper we present the construction of a group Hopf algebra on the class of rational tangles. A locally finite partial order on this class is introduced and a topology is generated. An interval coalgebra structure associated with the locally finite partial order is specified. Irrational and real tangles are introduced and their relation with rational tangles are studied. The existence of the maximal real tangle is described in detail.
- Published
- 2017