On generalized homology of Artin groups.
Broto, C., Vershinin, V.V. (2000)
Zapiski Nauchnykh Seminarov POMI
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Broto, C., Vershinin, V.V. (2000)
Zapiski Nauchnykh Seminarov POMI
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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.
Hu, Sze-Tsen (1960)
Portugaliae mathematica
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Oleg Viro (2004)
Fundamenta Mathematicae
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Mikhail Khovanov defined, for a diagram of an oriented classical link, a collection of groups labelled by pairs of integers. These groups were constructed as the homology groups of certain chain complexes. The Euler characteristics of these complexes are the coefficients of the Jones polynomial of the link. The original construction is overloaded with algebraic details. Most of the specialists use adaptations of it stripped off the details. The goal of this paper is to overview these...
S. K. Kaul (1970)
Colloquium Mathematicae
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Urs Stammbach (1972)
Mathematische Zeitschrift
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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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J. Aguadé, M. Castellet (1978)
Collectanea Mathematica
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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.
С.Л. Понтрягин (1942)
Matematiceskij sbornik
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Z. Fiedorowicz, T. Pirashvili (1995)
Mathematische Annalen
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A. Blanco, J. Majadas, A.G. Rodicio (1996)
Inventiones mathematicae
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R. NARASIMHAN (1966)
Inventiones mathematicae
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Dominique Arlettaz (1993)
Commentarii mathematici Helvetici
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Filippo Callegaro, Ivan Marin (2014)
Journal of the European Mathematical Society
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Complex braid groups are the natural generalizations of braid groups associated to arbitrary (finite) complex reflection groups. We investigate several methods for computing the homology of these groups. In particular, we get the Poincaré polynomial with coefficients in a finite field for one large series of such groups, and compute the second integral cohomology group for all of them. As a consequence we get non-isomorphism results for these groups.
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...