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Finiteness length and connectivity length for groups. (English) Zbl 1009.20048
Cossey, John (ed.) et al., Geometric group theory down under. Proceedings of a special year in geometric group theory, Canberra, Australia, July 14-19, 1996. Berlin: de Gruyter. 9-22 (1999).
The finiteness length \(\text{fl }G\) of a group \(G\) is the supremum of the natural numbers \(m\geq 0\) such that there is an Eilenberg-MacLane complex \(K(G,1)\) with finite \(m\)-skeleton. The author surveys results on the finiteness length of groups. He uses the concept of connectivity length to take a new look at \(\text{fl }G\). In this formulation the behavior of the finiteness length of direct products is much easier to explain and leads to a conjectured additivity formula for the connectivity length. The status and partial results on this conjecture are surveyed by the author.
For the entire collection see [Zbl 0910.00040].

MSC:
20F65 Geometric group theory
57M07 Topological methods in group theory
20J05 Homological methods in group theory
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