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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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...