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Novikov homology of HNN–extensions and right-angled Artin groups

Dirk Schütz

Algebraic & Geometric Topology 9 (2009) 773–809

We calculate the Novikov homology of right-angled Artin groups and certain HNN–extensions of these groups. This is used to obtain information on the homological Sigma invariants of Bieri–Neumann–Strebel–Renz for these groups. These invariants are subsets of all homomorphisms from a group to the reals containing information on the finiteness properties of kernels of such homomorphisms. We also derive information on the homotopical Sigma invariants and show that one cannot expect any symmetry relations between a homomorphism and its negative regarding these invariants. While it was previously known that these invariants are not symmetric in general, we give the first examples of homomorphisms which are symmetric with respect to the homological invariant, but not with respect to the homotopical invariant.

Novikov homology, HNN-extension, right-angled Artin group, Sigma invariants
Mathematical Subject Classification 2000
Primary: 20J05
Secondary: 20F65, 57R19
Received: 19 December 2008
Revised: 27 March 2009
Accepted: 29 March 2009
Published: 20 April 2009
Dirk Schütz
Department of Mathematics
University of Durham
Durham DH1 3LE