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Displaying similar documents to “Compact manifolds with exceptional holonomy.”

Singularities of non-degenerate n-ruled (n + 1)-manifolds in Euclidean space

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.

A homological selection theorem implying a division theorem for Q-manifolds

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...