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Relating the Farrell Nil-groups to the Waldhausen Nil-groups

J. -F. Lafont·I. J. Ortiz
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Abstract

We prove that the Waldhausen Nil-group associated to a virtually cyclic groups that surjects onto the infinite dihedral group vanishes if and only if the corresponding Farrell Nil-group associated to the canonical index two subgroup is trivial. The proof uses the transfer map to establish one direction, and uses controlled pseudo-isotopy techniques of Farrell-Jones to establish the reverse implication.

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BibTeXRIS

J. -F. Lafont, I. J. Ortiz. 2006-09-25. Relating the Farrell Nil-groups to the Waldhausen Nil-groups. https://arxiv.org/abs/math/0609711

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