Algebraic and topological structures on rational tangles


  • Vida Milani Utah State University
  • Seyed M.H. Mansourbeigi Utah State University
  • Hossein Finizadeh Shahid Beheshti University



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


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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Author Biographies

Vida Milani, Utah State University

Department of Mathematics and Statistics

Seyed M.H. Mansourbeigi, Utah State University

Department of Mathematics and Statistics

Hossein Finizadeh, Shahid Beheshti University

Department of Mathematics, Faculty of Mathematical Sciences


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How to Cite

V. Milani, S. M. Mansourbeigi, and H. Finizadeh, “Algebraic and topological structures on rational tangles”, Appl. Gen. Topol., vol. 18, no. 1, pp. 1–11, Apr. 2017.



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