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