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arXiv · 1002.3702

Algebraic K-theory over the infinite dihedral group: a controlled topology approach

James F. Davis·Frank Quinn·Holger Reich
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Abstract

We use controlled topology applied to the action of the infinite dihedral group on a partially compactified plane and deduce two consequences for algebraic K-theory. The first is that the family in the K-theoretic Farrell-Jones conjecture can be reduced to only those virtually cyclic groups which admit a surjection with finite kernel onto a cyclic group. The second is that the Waldhausen Nil groups for a group which maps epimorphically onto the infinite dihedral group can be computed in terms of the Farrell-Bass Nil groups of the index two subgroup which maps surjectively to the infinite cyclic group.

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BibTeXRIS

James F. Davis, Frank Quinn, Holger Reich. 2011-03-08. Algebraic K-theory over the infinite dihedral group: a controlled topology approach. https://doi.org/10.1112/jtopol%2Fjtr009

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