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

Vida Milani, Ali Asghar Rezaei, Seyed M.H. Mansourbeigi


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. Some examples are given to illustrate these geometric information. The main object of this work is a classification of unital C*-algebras by noncommutative CW complexes and the modified Morse functions on them.


C*-algebra; Critical points; CW complexes; Homotopy equivalence; Homotopy type; Morse function; Noncommutative CW complex; Poset; Pseudo-homotopy type; *-representation; Simplicial complex

Subject classification

06B30; 46L35; 46L85; 55P15; 55U10

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