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1
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Strong surjectivity of mappings of some 3-complexes into $$ M_{Q_8 } $$

100%
Aniz C.
Open Mathematics
|
2008
|
tom 6
|
nr 4
497-503
EN
Let K be a CW-complex of dimension 3 such that H 3(K;ℤ) = 0 and $$ M_{Q_8 } $$ the orbit space of the 3-sphere $$ \mathbb{S}^3 $$ with respect to the action of the quaternion group Q 8 determined by the inclusion Q 8 ⊆ $$ \mathbb{S}^3 $$. Given a point a ∈ $$ M_{Q_8 } $$, we show that there is no map f:K → $$ M_{Q_8 } $$ which is strongly surjective, i.e., such that MR[f,a]=min{#(g −1(a))|g ∈ [f]} ≠ 0.
2
Content available remote

Novikov homology, jump loci and Massey products

84%
Kohno T., Pajitnov A.
Open Mathematics
|
2014
|
tom 12
|
nr 9
1285-1304
EN
Let 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).
3
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On localization in holomorphic equivariant cohomology

68%
Bruzzo U., Rubtsov V.
Open Mathematics
|
2012
|
tom 10
|
nr 4
1442-1454
EN
We study a holomorphic equivariant cohomology built out of the Atiyah algebroid of an equivariant holomorphic vector bundle and prove a related localization formula. This encompasses various residue formulas in complex geometry, in particular we shall show that it contains as special cases Carrell-Liebermann’s and Feng-Ma’s residue formulas, and Baum-Bott’s formula for the zeroes of a meromorphic vector field.
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