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arXiv · 1906.03494

Asymptotic property C of the countable direct sum of uniformly discrete $0$-hyperbolic spaces

Kamil Orzechowski
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Abstract

We define the direct sum of a countable family of pointed metric spaces in a way resembling the direct sum of groups. Then we prove that if a family consists of $0$-hyperbolic (in the sense of Gromov) and $D$-discrete spaces, then its direct sum has asymptotic property C. The main example is a countable direct sum of free groups of (possibly varying) finite rank. This is a generalization of T. Yamauchi's result concernig the countable direct sum of the integers.

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Kamil Orzechowski. 2019-06-08. Asymptotic property C of the countable direct sum of uniformly discrete $0$-hyperbolic spaces. https://arxiv.org/abs/1906.03494

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