Algebraic and topological structures on rational tangles

Vida Milani, Seyed M.H. Mansourbeigi, Hossein Finizadeh

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.


Keywords

group Hopf algebra; locally finite partial order; tangle; pseudo-module; bi-pseudo-module; pseudo-tensor product; incidence algebra; interval coalgebra; continued fraction; tangle convergent.

Subject classification

16T05; 11Y65; 18B35; 57M27; 57T05.

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