Steenrod homology
Yu. T. Lisitsa, S. Mardešić (1986)
Banach Center Publications
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Yu. T. Lisitsa, S. Mardešić (1986)
Banach Center Publications
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Fred Richman (1976)
Fundamenta Mathematicae
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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...
M. V. Mielke (1993)
Commentationes Mathematicae Universitatis Carolinae
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In this paper we extend the Eilenberg-Steenrod axiomatic description of a homology theory from the category of topological spaces to an arbitrary category and, in particular, to a topos. Implicit in this extension is an extension of the notions of homotopy and excision. A general discussion of such homotopy and excision structures on a category is given along with several examples including the interval based homotopies and, for toposes, the excisions represented by “cutting out” subobjects....
J. Dugundji (1966)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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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...
Steven Garavaglia (1978)
Fundamenta Mathematicae
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Daryl George (1984)
Fundamenta Mathematicae
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S. K. Kaul (1970)
Colloquium Mathematicae
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