Amenable category and complexity
Pietro Capovilla, Clara Loeh, Marco Moraschini
TL;DR
This paper explores the properties of amenable category, a variant of Lusternik-Schnirelman category, focusing on its monotonicity, relation to topological complexity, and implications for degree-one maps.
Contribution
It investigates the monotonicity problem for amenable category and its connection with topological complexity, providing new insights into their interplay.
Findings
Established conditions for monotonicity of amenable category.
Analyzed the relationship between amenable category and topological complexity.
Provided results linking amenable category to degree-one maps.
Abstract
Amenable category is a variant of the Lusternik-Schnirelman category, based on covers by amenable open subsets. We study the monotonicity problem for degree-one maps and amenable category and the relation between amenable category and topological complexity.
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