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Rank gradients of infinite cyclic covers of Kähler manifolds

Friedl, Stefan ; Vidussi, Stefano



Abstract

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 ...

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