On homology planes and contractible 4-manifolds (Q6614904)

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scientific article; zbMATH DE number 7922704
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On homology planes and contractible 4-manifolds
scientific article; zbMATH DE number 7922704

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    On homology planes and contractible 4-manifolds (English)
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    8 October 2024
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    A Kirby-Ramanujam sphere is a nontrivial homology sphere which bounds both a homology plane and a Mazur or Poénaru manifold. The boundary of the Ramanujam surface [\textit{C. P. Ramanujam}, Ann. Math. (2) 94, 69--88 (1971; Zbl 0218.14021)] is the first example of such spheres. The present authors add systematically three more infinite series \(\partial X(n), \partial Y(n), \partial Z(n)\) of such spheres as the boundaries of homology planes constructed respectively by \textit{T. tom Dieck} and \textit{T. Petrie} [Prog. Math. 80, 27--48 (1989; Zbl 0708.14024)], \textit{M. G. Zaidenberg} [in: Colloque d'analyse complexe et géométrie. Marseille, France, 13-17 janvier 1992. Paris: Société Mathématique de France. 251--282; Appendix 260--282 (1993; Zbl 0801.14001)] and \textit{R. V. Gurjar} and \textit{M. Miyanishi} [in: Algebraic geometry and commutative algebra, Vol. I. 99--124 (1988; Zbl 0707.14015)].
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    Kirby-Ramanujam sphere, homology sphere, boundary ,Mazur or Poenaru manifold, homology plane,
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