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

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. 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.

Keywords

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