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

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

2006-09-25

arxiv.org/abs/math/0609711v1

Forum Math. 20 (2008), pgs. 445-455

Mathematics

K-Theory and Homology

10 pages

Scientific paper

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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