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• W3131456989 abstract "We study asymptotic invariants of metric spaces, defined in terms of the travelling salesman problem, and our goal is to classify groups and spaces depending on how well they can be ordered in this context. We characterize virtually free groups as those admitting an order which has some efficiency on $4$-point subsets. We show that all $delta$-hyperbolic spaces can be ordered extremely efficiently, for the question when the number of points of a subset tends to $infty$. We prove that all spaces of finite Assouad-Nagata dimension admit a good order for the above mentioned problem, and under an additional hypothesis we prove the converse. Despite travelling salesman terminology, our paper does not aim at applications in computer science. Our goal is to study new properties of groups and metric spaces, and describe their connection with more traditional invariants, such as hyperbolicity, dimension, number of ends and doubling." @default.
• W3131456989 created "2021-03-01" @default.
• W3131456989 creator A5038556026 @default.
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• W3131456989 date "2020-11-03" @default.
• W3131456989 modified "2023-09-27" @default.
• W3131456989 title "Hyperbolicity, Assouad-Nagata dimension and orders on metric spaces" @default.
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• W3131456989 hasPublicationYear "2020" @default.
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