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Topological tameness conditions of spaces and groups: Results and developments∗

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Abstract

We present a general survey of several conditions and results related to the topology at infinity of manifolds, and of the corresponding notions adapted to finitely presented groups, focusing mainly on topological “tameness” conditions coming from low-dimensional topology. In particular, we describe and study connectivity properties at infinity and several notions of geometric (simple) connectivity, together with their generalizations, in a wide sense, to discrete groups. Moreover, for each of these notions, we also introduce suitable functions measuring the rates of growth of the spaces involved.

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  1. Institute of Mathematics and Informatics, Vilnius University, Akademijos str. 4, LT-08663, Vilnius, Lithuania

    Daniele Ettore Otera

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Correspondence to Daniele Ettore Otera.

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∗ The author was supported by the Research Council of Lithuania, grant No. MIP-046/2014/LSS-580000-446 (Researcher teams’ projects).

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Otera, D.E. Topological tameness conditions of spaces and groups: Results and developments∗ . Lith Math J 56, 357–376 (2016). https://doi.org/10.1007/s10986-016-9323-2

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