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Topological Type in Families of Germs.

Henry C. King (1980/1981)

Inventiones mathematicae

Topology of Fatou components for endomorphisms of $ℂ ℙ^{k}$ : linking with the Green’s current

Suzanne Lynch Hruska, Roland K. W. Roeder (2010)

Fundamenta Mathematicae

Little is known about the global topology of the Fatou set U(f) for holomorphic endomorphisms $f : ℂ ℙ^{k} \to ℂ ℙ^{k}$ , when k >1. Classical theory describes U(f) as the complement in $ℂ ℙ^{k}$ of the support of a dynamically defined closed positive (1,1) current. Given any closed positive (1,1) current S on $ℂ ℙ^{k}$ , we give a definition of linking number between closed loops in $ℂ ℙ^{k} ∖ s u p p S$ and the current S. It has the property that if lk(γ,S) ≠ 0, then γ represents a non-trivial homology element in $H ₁ (ℂ ℙ^{k} ∖ s u p p S)$ . As an application, we use these linking...

Topology of the complement of real hyperplanes in CN.

M. Salvetti (1987)

Inventiones mathematicae

Toward a general theory of linking invariants.

Chernov, Vladimir V., Rudyak, Yuli B. (2005)

Geometry & Topology

Truncated symmetric products and configuration spaces.

C.-F. Bödigheimer, F.R. Cohen (1993)

Mathematische Zeitschrift

Über den Homotopietyp von Linsenraumprodukten

Günther Huck, Wolfgang Metzler (1985)

Fundamenta Mathematicae

Vanishing theorems for compact hessian manifolds

Hirohiko Shima (1986)

Annales de l'institut Fourier

A manifold is said to be Hessian if it admits a flat affine connection $D$ and a Riemannian metric $g$ such that $g = D^{2} u$ where $u$ is a local function. We study cohomology for Hessian manifolds, and prove a duality theorem and vanishing theorems.