Morse Theory for C*-Algebras: A Geometric Interpretation of Some Noncommutative Manifolds

2009/12/13 by Vida Milani, Milani, Vida, Seyed M. H. Mansourbeigi +3
Mathematics · #06B30 #46L35 #46L85 #55P15 #55U10 #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric Topology (math.GT) #math.AT #math.GT #msc:06B30 #msc:46L35 #msc:46L85 #msc:55P15 #msc:55U10

paper · pdf · doi:10.48550/arxiv.0912.2471

18 pages

arxiv created 2010/01/18 · arxiv updated 2010/02/08

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.

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