Displaying similar documents to “On the homology groups of q -complete spaces”

On q -Runge pairs

Mihnea Colţoiu (2003)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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We show that the converse of the aproximation theorem of Andreotti and Grauert does not hold. More precisely we construct a 4 -complete open subset D ⊂ ℂ 6 (which is an analytic complement in the unit ball) such that the restriction map H 3 ( ℂ 6 , ℱ ) → H 3 ( D , ℱ ) has a dense image for every ℱ ∈ C o h ( ℂ 6 ) but the pair ( D , ℂ 6 ) is not a 4 -Runge pair.

Torsion of Khovanov homology

Alexander N. Shumakovitch (2014)

Fundamenta Mathematicae

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Khovanov homology is a recently introduced invariant of oriented links in ℝ³. It categorifies the Jones polynomial in the sense that the (graded) Euler characteristic of Khovanov homology is a version of the Jones polynomial for links. In this paper we study torsion of Khovanov homology. Based on our calculations, we formulate several conjectures about the torsion and prove weaker versions of the first two of them. In particular, we prove that all non-split alternating links have their...

Runge families and inductive limits of Stein spaces

Andrew Markoe (1977)

Annales de l'institut Fourier

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The general Stein union problem is solved: given an increasing sequence of Stein open sets, it is shown that the union X is Stein if and only if H 1 ( X , O X ) is Hausdorff separated.

Torsion in Khovanov homology of semi-adequate links

Józef H. Przytycki, Radmila Sazdanović (2014)

Fundamenta Mathematicae

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The goal of this paper is to address A. Shumakovitch's conjecture about the existence of ℤ₂-torsion in Khovanov link homology. We analyze torsion in Khovanov homology of semi-adequate links via chromatic cohomology for graphs, which provides a link between link homology and the well-developed theory of Hochschild homology. In particular, we obtain explicit formulae for torsion and prove that Khovanov homology of semi-adequate links contains ℤ₂-torsion if the corresponding Tait-type graph...

Torsion in one-term distributive homology

Alissa S. Crans, Józef H. Przytycki, Krzysztof K. Putyra (2014)

Fundamenta Mathematicae

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The one-term distributive homology was introduced in [Prz] as an atomic replacement of rack and quandle homology, which was first introduced and developed by Fenn-Rourke-Sanderson [FRS] and Carter-Kamada-Saito [CKS]. This homology was initially suspected to be torsion-free [Prz], but we show in this paper that the one-term homology of a finite spindle may have torsion. We carefully analyze spindles of block decomposition of type (n,1) and introduce various techniques to compute their...