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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Bruns, Winfried, Vetter, Udo (1998)
Beiträge zur Algebra und Geometrie
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Takuma Imamura (2021)
Archivum Mathematicum
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In this paper, we clarify the relationship among the Vietoris-type homology theories and the microsimplicial homology theories, where the latter are nonstandard homology theories defined by M.C. McCord (for topological spaces), T. Korppi (for completely regular topological spaces) and the author (for uniform spaces). We show that McCord’s and our homology are isomorphic for all compact uniform spaces and that Korppi’s and our homology are isomorphic for all fine uniform spaces. Our homology...
Brooke E. Shipley (1995)
Mathematische Zeitschrift
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Yu. T. Lisitsa, S. Mardešić (1986)
Banach Center Publications
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Hans Ligaard, Ib Madsen (1975)
Mathematische Zeitschrift
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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...
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.
Douglas C. Ravenel (1993)
Forum mathematicum
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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.
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.
Bijan Sahamie (2013)
Annales de la faculté des sciences de Toulouse Mathématiques
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This paper provides an introduction to the basics of Heegaard Floer homology with some emphasis on the hat theory and to the contact geometric invariants in the theory. The exposition is designed to be comprehensible to people without any prior knowledge of the subject.
Stefano De Michelis (1991)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
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We study the homology of the fixed point set on a rational homology sphere under the action of a finite group.
Steven Garavaglia (1978)
Fundamenta Mathematicae
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A. Blanco, J. Majadas, A.G. Rodicio (1996)
Inventiones mathematicae
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Levine, Jerome (2001)
Algebraic & Geometric Topology
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