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

Authors

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

DOI:

https://doi.org/10.4995/agt.2011.1650

Keywords:

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

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.

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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.

vmilani3@math.gatech.edu

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

[1]
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.

Issue

Vol. 12 No. 2 (2011)

Section

Regular Articles

License

This journal is licensed under a  Creative Commons Attribution-NonCommercial-ShareAlike- 4.0 International License.

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