Zusammenfassung
Given a Kahler group G and a primitive class phi is an element of H-1 (G; Z), we show that the rank gradient of (G, phi) is zero if and only if Ker phi <= G is finitely generated. Using this approach, we give a quick proof of the fact (originally due to Napier and Ramachandran) that Kahler groups are not properly ascending or descending HNN extensions. Further investigation of the properties of ...
Zusammenfassung
Given a Kahler group G and a primitive class phi is an element of H-1 (G; Z), we show that the rank gradient of (G, phi) is zero if and only if Ker phi <= G is finitely generated. Using this approach, we give a quick proof of the fact (originally due to Napier and Ramachandran) that Kahler groups are not properly ascending or descending HNN extensions. Further investigation of the properties of Bieri-Neumann-Strebel invariants of Kahler groups allows us to show that a large class of groups of orientation-preserving PL homeomorphisms of an interval (customarily denoted F(l, Z[1/n(1)...n(k)], < n(1),...,n(k) >)), which generalize Thompson's group F, are not Kahler.
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