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Journal of the London Mathematical Society Advance Access originally published online on January 6, 2009
Journal of the London Mathematical Society 2009 79(2):309-322; doi:10.1112/jlms/jdn075
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© 2009 London Mathematical Society

Splitting formulas for certain Waldhausen Nil-groups

Jean-François Lafont

Department of Mathematics
Ohio State University
Columbus, OH 43210
USA

Ivonne J. Ortiz

Department of Mathematics and Statistics
Miami University
Oxford, OH 45056
USA
ortizi@muohio.edu

We provide splitting formulas for certain Waldhausen Nil-groups. We focus on Waldhausen Nil-groups associated to acylindrical amalgamations {Gamma} = G1 * H G2 of the groups G1 and G2 over a common subgroup H. For these amalgamations, we explain how, provided that G1, G2 and {Gamma} satisfy the Farrell–Jones isomorphism conjecture, the Waldhausen Nil-groups NilFormula(RH; R[G1 – H], R[G2 – H]) can be expressed as a direct sum of Nil-groups associated to a specific collection of virtually cyclic subgroups of {Gamma}. A special case covered by our theorem is the case of arbitrary amalgamations over a finite group H.

2000 Mathematics Subject Classification 18F25 (primary), 20E08 (secondary).

This research was partly supported by the NSF, under grants DMS-0606002 and DMS-0805605. The first author was partly supported by an Alfred P. Sloan research fellowship.

Received January 1, 2008; revised July 14, 2008; published online January 6, 2009.


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