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

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

2009-12-13

arxiv.org/abs/0912.2471v2

Mathematics

Algebraic Topology

18 pages

Scientific paper

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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