Some results and conjectures on finite groups acting on homology spheres.
Zimmermann, B.P. (2005)
Sibirskie Ehlektronnye Matematicheskie Izvestiya [electronic only]
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Zimmermann, B.P. (2005)
Sibirskie Ehlektronnye Matematicheskie Izvestiya [electronic only]
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Reinhard Schultz (1985)
Manuscripta mathematica
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Mikio Furuta (1990)
Inventiones mathematicae
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Ronald M., Hamrick, Gary C. Dotzel (1980/81)
Inventiones mathematicae
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Bruno P. Zimmermann (2004)
Fundamenta Mathematicae
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We show that, if the covering involution of a 3-manifold M occurring as the 2-fold branched covering of a knot in the 3-sphere is contained in a finite nonabelian simple group G of diffeomorphisms of M, then M is a homology 3-sphere and G isomorphic to the alternating or dodecahedral group 𝔸₅ ≅ PSL(2,5). An example of such a 3-manifold is the spherical Poincaré sphere. We construct hyperbolic analogues of the Poincaré sphere. We also give examples of hyperbolic ℤ₂-homology 3-spheres...
Jean-Luc Brylinski (1987)
Annales de l'institut Fourier
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In this article, we present two possible extensions of the classical theory of equivariant cohomology. The first, due to P. Baum, R. MacPherson and the author, is called the “delocalized theory". We attempt to present it in very concrete form for a circle action on a smooth manifold. The second is the cyclic homology of the crossed- product algebra of the algebra of smooth functions on a manifold, by the convolution algebra of smooth functions on a Lie group, when such Lie group act...
S. K. Kaul (1970)
Colloquium Mathematicae
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Elhamdadi, Mohamed (2001)
International Journal of Mathematics and Mathematical Sciences
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Czes Kosniowski (1983)
Mathematische Zeitschrift
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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.
Bruns, Winfried, Vetter, Udo (1998)
Beiträge zur Algebra und Geometrie
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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.