On the Homology Structure of Submersions.
J. Wolfgang SMITH (1971)
Mathematische Annalen
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J. Wolfgang SMITH (1971)
Mathematische Annalen
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Karlheinz Knapp (1978)
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Z. Fiedorowicz, T. Pirashvili (1995)
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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.
Christian Kassel, M. Vigué-Poirrier (1992)
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J.-C. Hausmann (1986)
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S. K. Kaul (1970)
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R.E. STONG (1970)
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Bruns, Winfried, Vetter, Udo (1998)
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Ernst Kunz, Siegfried Brüderle (1994)
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Heinz-Werner Schülting (1985)
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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...
Ludger Kaup, Karl-Heinz Fieseler (1988)
Mathematische Zeitschrift
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A. Blanco, J. Majadas, A.G. Rodicio (1996)
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Yu. T. Lisitsa, S. Mardešić (1986)
Banach Center Publications
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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.