Group actions on homology spheres.
J.F. Davis, S. Weinberger (1986)
Inventiones mathematicae
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J.F. Davis, S. Weinberger (1986)
Inventiones mathematicae
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Ronald M., Hamrick, Gary C. Dotzel (1980/81)
Inventiones mathematicae
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Reinhard Schultz (1985)
Manuscripta mathematica
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Zimmermann, B.P. (2005)
Sibirskie Ehlektronnye Matematicheskie Izvestiya [electronic only]
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Mikio Furuta (1990)
Inventiones mathematicae
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Stefano De Michelis (1991)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
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We study the homology of the fixed point set on a rational homology sphere under the action of a finite group.
Allan L. Edmonds (2009)
Colloquium Mathematicae
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The standard P. A. Smith theory of p-group actions on spheres, disks, and euclidean spaces is extended to the case of p-group actions on tori (i.e., products of circles) and coupled with topological surgery theory to give a complete topological classification, valid in all dimensions, of the locally linear, orientation-reversing, involutions on tori with fixed point set of codimension one.
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...
R.J. Stern, R. Fintushel (1987)
Inventiones mathematicae
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Mattia Mecchia (2004)
Fundamenta Mathematicae
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It is known that a finite 2-group acting on a ℤ₂-homology 3-sphere has at most ten conjugacy classes of involutions; the action of groups with the maximal number of conjugacy classes of involutions is strictly related to some questions concerning the representation of hyperbolic 3-manifolds as 2-fold branched coverings of knots. Using a low-dimensional approach we classify these maximal actions both from an algebraic and from a geometrical point of view.
Eldar Straume (1990)
Mathematica Scandinavica
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Hans Jorgen Munkholm (1969)
Mathematica Scandinavica
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Shinji Fukuhara, Yukio Matsumoto (1990)
Mathematische Annalen
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Alexander I. Suciu (1987)
Mathematische Zeitschrift
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