A noncommutative version of Farber's topological complexity
Copyright policy )A noncommutative version of Farber's topological complexity
Topological complexity for spaces was introduced by M. Farber as a minimal number of continuity domains for motion planning algorithms. It turns out that this notion can be extended to the case of not necessarily commutative C*-algebras. Topological complexity for spaces is closely related to the Lusternik--Schnirelmann category, for which we do not know any noncommutative extension, so there is no hope to generalize the known estimation methods, but we are able to evaluate the topological complexity for some very simple examples of noncommutative C*-algebras.
9 pages; minor mistakes removed; to appear in Topological Methods in Nonlinear Analysis
General theory of \(C^*\)-algebras, 46L05, 46L80, \(C^\ast\)-algebra, homotopy, Mathematics - Operator Algebras, FOS: Mathematics, topological complexity, Noncommutative topology, Operator Algebras (math.OA)
General theory of \(C^*\)-algebras, 46L05, 46L80, \(C^\ast\)-algebra, homotopy, Mathematics - Operator Algebras, FOS: Mathematics, topological complexity, Noncommutative topology, Operator Algebras (math.OA)
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).0 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Average influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Average impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!