Analog category and complexity. (English) Zbl 07902822
Summary: We study probabilistic variants of the Lusternik-Schnirelmann category and topological complexity, which bound the classical invariants from below. We present a number of computations illustrating both wide agreement and wide disagreement with the classical notions. In the aspherical case, where our invariants are group invariants, we establish a counterpart of the Eilenberg-Ganea theorem in the torsion-free case, as well as a contrasting universal upper bound in the finite case.
MSC:
| 55M30 | Lyusternik-Shnirel’man category of a space, topological complexity à la Farber, topological robotics (topological aspects) |
| 60B05 | Probability measures on topological spaces |
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