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math.OA2016
A noncommutative version of Farber's topological complexity
Vladimir Manuilov
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 extende…
math.KT2016
Balanced pairs of operators and their relative index
Vladimir Manuilov
We show that the K_1 group of a C*-algebra can be defined as homotopy classes of pairs, called balanced, of not necessarily unitary matrices over that have equal defects fr…