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


  • Vida Milani Shahid Beheshti University
  • Ali Asghar Rezaei Shahid Beheshti University
  • Seyed M.H. Mansourbeigi Polytechnic University NY



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


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.


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Author Biographies

Vida Milani, Shahid Beheshti University

Dept. of Math., Faculty of Math. Sci., Shahid Beheshti University, Tehran, Iran.

School of Mathematics, Georgia Institute of Technology, Atlanta GA, USA.

Ali Asghar Rezaei, Shahid Beheshti University

Dept. of Math., Faculty of Math. Sci.

Seyed M.H. Mansourbeigi, Polytechnic University NY

Dept. of Electrical Engineering


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How to Cite

V. Milani, A. A. Rezaei, and S. M. Mansourbeigi, “Morse theory for C*-algebras: a geometric interpretation of some noncommutative manifolds”, Appl. Gen. Topol., vol. 12, no. 2, pp. 175–185, Oct. 2011.



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