Some results on -manifolds.
Di Terlizzi, Luigia, Pastore, Anna Maria (2002)
Balkan Journal of Geometry and its Applications (BJGA)
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Di Terlizzi, Luigia, Pastore, Anna Maria (2002)
Balkan Journal of Geometry and its Applications (BJGA)
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Joyce, Dominic (1998)
Documenta Mathematica
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Alberto Tognoli (2003)
Bollettino dell'Unione Matematica Italiana
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We study the problem of approximating, up to homotopy, compact topological manifolds by real algebraic varieties. As a consequence, we realize any integral non-degenerate quadratic form as the intersection form of a real algebraic variety. This is related to a well-known result, due to Freedman [F], on the topology of closed simply-connected topological -manifolds.
Juraj Lörinc (2003)
Mathematica Slovaca
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Freedman, Michael H., Kitaev, Alexei, Nayak, Chetan, Slingerland, Johannes K., Walker, Kevin, Wang, Zhenghan (2005)
Geometry & Topology
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R. Ayala, A. Quintero (1992)
Collectanea Mathematica
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Rezaii, M.M., Barzegari, M. (2006)
Balkan Journal of Geometry and its Applications (BJGA)
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Taras Banakh, Robert Cauty (2007)
Banach Center Publications
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We prove that a space M with Disjoint Disk Property is a Q-manifold if and only if M × X is a Q-manifold for some C-space X. This implies that the product M × I² of a space M with the disk is a Q-manifold if and only if M × X is a Q-manifold for some C-space X. The proof of these theorems exploits the homological characterization of Q-manifolds due to Daverman and Walsh, combined with the existence of G-stable points in C-spaces. To establish the existence of such points we prove (and...
Kentaro Saji (2004)
Banach Center Publications
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The objective of this paper is to study singularities of n-ruled (n + 1)-manifolds in Euclidean space. They are one-parameter families of n-dimensional affine subspaces in Euclidean space. After defining a non-degenerate n-ruled (n + 1)-manifold we will give a necessary and sufficient condition for such a map germ to be right-left equivalent to the cross cap × interval. The behavior of a generic n-ruled (n + 1)-manifold is also discussed.
James Eells, Nicolaas H. Kuiper (1962)
Publications Mathématiques de l'IHÉS
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