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Topological realization of a family of pseudoreflection groups

Dietrich Notbohm (1998)

Fundamenta Mathematicae

We are interested in a topological realization of a family of pseudoreflection groups G G L ( n , F p ) ; i.e. we are looking for topological spaces whose mod-p cohomology is isomorphic to the ring of invariants F p [ x 1 , . . . , x n ] G . Spaces of this type give partial answers to a problem of Steenrod, namely which polynomial algebras over F p can appear as the mod-p cohomology of a space. The family under consideration is given by pseudoreflection groups which are subgroups of the wreath product / q Σ n where q divides p - 1 and where p is...

Topology and dynamics of unstable attractors

M. A. Morón, J. J. Sánchez-Gabites, J. M. R. Sanjurjo (2007)

Fundamenta Mathematicae

This article aims to explore the theory of unstable attractors with topological tools. A short topological analysis of the isolating blocks for unstable attractors with no external explosions leads quickly to sharp results about their shapes and some hints on how Conley's index is related to stability. Then the setting is specialized to the case of flows in ℝⁿ, where unstable attractors are seen to be dynamically complex since they must have external explosions.

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