Geodesic
Novikov homology of HNN–extensions and right-angled Artin groups
Schütz, Dirk1
1 Department of Mathematics, University of Durham, Durham DH1 3LE, UK
Algebraic and Geometric Topology, Tome 9 (2009) no. 2, pp. 773-809

Voir la notice de l'article provenant de la source Mathematical Sciences Publishers

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.

DOI : 10.2140/agt.2009.9.773
Keywords: Novikov homology, HNN-extension, right-angled Artin group, Sigma invariants

Schütz, Dirk 1

1 Department of Mathematics, University of Durham, Durham DH1 3LE, UK 
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Schütz, Dirk. Novikov homology of HNN–extensions and right-angled Artin groups. Algebraic and Geometric Topology, Tome 9 (2009) no. 2, pp. 773-809. doi: 10.2140/agt.2009.9.773

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