Algebraic and topological structures on rational tangles

Vida Milani

United States

Utah State University

Department of Mathematics and Statistics

Seyed M.H. Mansourbeigi

United States

Utah State University

Department of Mathematics and Statistics

Hossein Finizadeh

Iran, Islamic Republic of

Shahid Beheshti University

Department of Mathematics, Faculty of Mathematical Sciences
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Accepted: 2016-11-22

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Published: 2017-04-03

DOI: https://doi.org/10.4995/agt.2017.2250
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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.

Supporting agencies:

This research was not funded

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.

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