Polynomial periodicity for Betti numbers of covering surfaces.
Alexander stratifications of character varieties
Equations defining the jumping loci for the first cohomology group of one-dimensional representations of a finitely presented group can be effectively computed using Fox calculus. In this paper, we give an exposition of Fox calculus in the language of group cohomology and in the language of finite abelian coverings of CW complexes. Work of Arapura and Simpson imply that if is the fundamental group of a compact Kähler manifold, then the strata are finite unions of translated affine subtori. It...
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