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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 the boundary of 2-dimensional ideal polyhedra

Emmanuel Vrontakis (2006)

Commentationes Mathematicae Universitatis Carolinae

It is proved that for every two points in the visual boundary of the universal covering of a 2 -dimensional ideal polyhedron, there is an infinity of paths joining them.

On the connectivity of skeletons of pseudomanifolds with boundary

R. Ayala, M. J. Chávez, Alberto Márquez, Antonio Quintero (2002)

Mathematica Bohemica

In this note we show that 1 -skeletons and 2 -skeletons of n -pseudomanifolds with full boundary are ( n + 1 ) -connected graphs and n -connected 2 -complexes, respectively. This generalizes previous results due to Barnette and Woon.

Optics in Croke-Kleiner Spaces

Fredric D. Ancel, Julia M. Wilson (2010)

Bulletin of the Polish Academy of Sciences. Mathematics

We explore the interior geometry of the CAT(0) spaces X α : 0 < α π / 2 , constructed by Croke and Kleiner [Topology 39 (2000)]. In particular, we describe a diffraction effect experienced by the family of geodesic rays that emanate from a basepoint and pass through a certain singular point called a triple point, and we describe the shadow this family casts on the boundary. This diffraction effect is codified in the Transformation Rules stated in Section 3 of this paper. The Transformation Rules have various applications....

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