Year: 2025
Type: article
Abstract: In this paper, we develop the theory of probabilistic variants of the one-category and diagonal topological complexity, which bound the classical LS-category and topological complexity from below. Unlike any other classical or probabilistic invariants, these invariants are rigid on spaces with finite fundamental group. On Eilenberg–Mac Lane spaces, we identify these new invariants with distributional category and complexity, respectively, and use them to illuminate aspects of the behavior of the latter invariants on aspherical spaces and products of spaces. We also study their properties on covering maps, [Formula: see text]-isomorphisms, [Formula: see text]-spaces, and closed essential manifolds, and consequently, obtain the first examples of closed manifolds beyond the real projective spaces on which the distributional theory disagrees with the classical one.
Source: Journal of Topology and Analysis
Authors: Ekansh Jauhari, John Oprea
Institutions: University of Florida, Cleveland State University
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4417517533
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