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On deformations of spherical isometric foldings

Ana M. Breda, Altino F. Santos (2010)

Czechoslovak Mathematical Journal

The behavior of special classes of isometric foldings of the Riemannian sphere S 2 under the action of angular conformal deformations is considered. It is shown that within these classes any isometric folding is continuously deformable into the standard spherical isometric folding f s defined by f s ( x , y , z ) = ( x , y , | z | ) .

On equivariant deformations of maps.

Antonio Vidal (1988)

Publicacions Matemàtiques

We work in the smooth category: manifolds and maps are meant to be smooth. Let G be a finite group acting on a connected closed manifold X and f an equivariant self-map on X with f|A fixpointfree, where A is a closed invariant submanifold of X with codim A ≥ 3. The purpose of this paper is to give a proof using obstruction theory of the following fact: If X is simply connected and the action of G on X - A is free, then f is equivariantly deformable rel. A to fixed point free map if and only if the...

On extension of functors

L. Karchevska, Taras Radul (2012)

Commentationes Mathematicae Universitatis Carolinae

A. Chigogidze defined for each normal functor on the category Comp an extension which is a normal functor on the category Tych. We consider this extension for any functor on the category Comp and investigate which properties it preserves from the definition of normal functor. We investigate as well some topological properties of such extension.

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