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Abstract
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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.
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Keywords
Novikov homology, HNN-extension, right-angled Artin group,
Sigma invariants
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Mathematical Subject Classification 2000
Primary: 20J05
Secondary: 20F65, 57R19
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Publication
Received: 19 December 2008
Revised: 27 March 2009
Accepted: 29 March 2009
Published: 20 April 2009
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