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

Schütz, Dirk

doi:10.2140/agt.2009.9.773

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

Dirk Schütz

Algebraic & Geometric Topology 9 (2009) 773–809

DOI: 10.2140/agt.2009.9.773

Abstract

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.

Keywords

Novikov homology, HNN-extension, right-angled Artin group, Sigma invariants

Mathematical Subject Classification 2000

Primary: 20J05

Secondary: 20F65, 57R19

References

Publication

Received: 19 December 2008

Revised: 27 March 2009

Accepted: 29 March 2009

Published: 20 April 2009

Authors

Dirk Schütz
Department of Mathematics University of Durham Durham DH1 3LE UK
http://www.maths.dur.ac.uk/~dma0ds/

Volume 9, issue 2 (2009)