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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