A characterization of the Čech homology theory
S. K. Kaul (1970)
Colloquium Mathematicae
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S. K. Kaul (1970)
Colloquium Mathematicae
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Yu. T. Lisitsa, S. Mardešić (1986)
Banach Center Publications
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Marian Mrozek, Bogdan Batko (2010)
Annales Polonici Mathematici
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We generalize the notion of cubical homology to the class of locally compact representable sets in order to propose a new convenient method of reducing the complexity of a set while computing its homology.
Bruns, Winfried, Vetter, Udo (1998)
Beiträge zur Algebra und Geometrie
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Z. Fiedorowicz, T. Pirashvili (1995)
Mathematische Annalen
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Daniel Krasner (2009)
Fundamenta Mathematicae
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We investigate the Khovanov-Rozansky invariant of a certain tangle and its compositions. Surprisingly the complexes we encounter reduce to ones that are very simple. Furthermore, we discuss a "local" algorithm for computing Khovanov-Rozansky homology and compare our results with those for the "foam" version of sl₃-homology.
S. Dragotti, G. Magro, L. Parlato (2006)
Bollettino dell'Unione Matematica Italiana
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We give, here, a geometric treatment of intersection homology theory.
A. Blanco, J. Majadas, A.G. Rodicio (1996)
Inventiones mathematicae
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Gregory R. Conner, Samuel M. Corson (2016)
Fundamenta Mathematicae
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We show that the first homology group of a locally connected compact metric space is either uncountable or finitely generated. This is related to Shelah's well-known result (1988) which shows that the fundamental group of such a space satisfies a similar condition. We give an example of such a space whose fundamental group is uncountable but whose first homology is trivial, showing that our result does not follow from Shelah's. We clarify a claim made by Pawlikowski (1998) and offer...
Krzysztof K. Putyra (2014)
Banach Center Publications
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We create a framework for odd Khovanov homology in the spirit of Bar-Natan's construction for the ordinary Khovanov homology. Namely, we express the cube of resolutions of a link diagram as a diagram in a certain 2-category of chronological cobordisms and show that it is 2-commutative: the composition of 2-morphisms along any 3-dimensional subcube is trivial. This allows us to create a chain complex whose homotopy type modulo certain relations is a link invariant. Both the original and...
Reinhold Hübl (1992)
Manuscripta mathematica
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Karl Heinz Fieseler, Ludger Kaup (1988)
Banach Center Publications
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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...
R. Mark Goresky (1984)
Commentarii mathematici Helvetici
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Steven Garavaglia (1978)
Fundamenta Mathematicae
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Magnus Jacobsson (2004)
Fundamenta Mathematicae
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We present an elementary description of Khovanov's homology of tangles [K2], in the spirit of Viro's paper [V]. The formulation here is over the polynomial ring ℤ[c], unlike [K2] where the theory was presented over the integers only.
D.E. Galewski, R.J. Stern (1977)
Inventiones mathematicae
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Chung-Wu Ho (1975)
Colloquium Mathematicae
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