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arXiv · 2401.15667

Analog category and complexity

Ben Knudsen·Shmuel Weinberger
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Abstract

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.

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Ben Knudsen, Shmuel Weinberger. 2024-01-28. Analog category and complexity. https://arxiv.org/abs/2401.15667

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