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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

2. Morse theory for C*-algebras: a geometric interpretation of some noncommutative manifolds

Author

Seyed M.H. Mansourbeigi, Vida Milani, Ali Rezaei, and Poli Paper

Subjects
Discrete Morse theory, 06B30, 46L35, 46L85, 55P15, 55U10, Critical points, lcsh:Analysis, C*-algebra, Interpretation (model theory), representation, Mathematics - Geometric Topology, Physical Sciences and Mathematics, FOS: Mathematics, Algebraic Topology (math.AT), Homotopy equivalence, Noncommutative algebraic geometry, Mathematics - Algebraic Topology, Simplicial complex, Handlebody, Circle-valued Morse theory, Morse theory, Mathematics, CW complexes, Computer Sciences, lcsh:Mathematics, lcsh:QA299.6-433, Pseudo-homotopy type, Geometric Topology (math.GT), lcsh:QA1-939, Noncommutative geometry, Homotopy type, Algebra, Poset, Noncommutative CW complex, Morse function, Geometry and Topology, Noncommutative quantum field theory
Abstract

The approach we present is a modification of the Morse theory for unital C*-algebras. We provide tools for the geometric interpretation of noncommutative CW complexes. These objects were introduced and studied in [2],[7] and [14]. Some examples to illustrate these geometric information in practice are given. A classification of unital C*-algebras by noncommutative CW complexes and the modified Morse functions on them is the main object of this work., 18 pages

Published
2011