Author:
Kohno Toshitake,Pajitnov Andrei
Abstract
AbstractLet X be a finite CW complex, and ρ: π 1(X) → GL(l, ℂ) a representation. Any cohomology class α ∈ H 1(X, ℂ) gives rise to a deformation γ t of ρ defined by γ t (g) = ρ(g) exp(t〈α, g〉). We show that the cohomology of X with local coefficients γ gen corresponding to the generic point of the curve γ is computable from a spectral sequence starting from H*(X, ρ). We compute the differentials of the spectral sequence in terms of the Massey products and show that the spectral sequence degenerates in case when X is a Kähler manifold and ρ is semi-simple.If α ∈ H 1(X, ℝ) one associates to the triple (X, ρ, α) the twisted Novikov homology (a module over the Novikov ring). We show that the twisted Novikov Betti numbers equal the Betti numbers of X with coefficients in the local system γ gen. We investigate the dependence of these numbers on α and prove that they are constant in the complement to a finite number of proper vector subspaces in H 1(X, ℝ).
Reference25 articles.
1. Arapura D., Higgs line bundles, Green-Lazarsfeld sets, and maps of Kähler manifolds to curves, Bull. Amer. Math. Soc. (N.S.), 1992, 26(2), 310–314
2. Benson C., Gordon C.S., Kähler structures on compact solvmanifolds, Proc. Amer. Math. Soc., 1990, 108(4), 971–980
3. Mem. Amer. Math. Soc.;AK Bousfield,1976
4. Deligne P., Griffiths Ph., Morgan J., Sullivan D., Real homotopy theory of Kähler manifolds, Invent. Math., 1975, 29(3), 245–274
5. Dimca A., Papadima S., Nonabelian cohomology jump loci from an analytic viewpoint, preprint avaliable at http://arxiv.org/abs/1206.3773
Cited by
5 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献