Algebraic K-theory over the infinite dihedral group: a controlled topology approach - Mathematics > K-Theory and HomologyReport as inadecuate




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



Author: James F. Davis, Frank Quinn, Holger Reich

Source: https://arxiv.org/







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