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Group actions on rational homology spheres

Stefano De Michelis (1991)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

We study the homology of the fixed point set on a rational homology sphere under the action of a finite group.

Involutions of 3-dimensional handlebodies

Andrea Pantaleoni, Riccardo Piergallini (2011)

Fundamenta Mathematicae

We study the orientation preserving involutions of the orientable 3-dimensional handlebody H g , for any genus g. A complete classification of such involutions is given in terms of their fixed points.

Involutions on tori with codimension-one fixed point set

Allan L. Edmonds (2009)

Colloquium Mathematicae

The standard P. A. Smith theory of p-group actions on spheres, disks, and euclidean spaces is extended to the case of p-group actions on tori (i.e., products of circles) and coupled with topological surgery theory to give a complete topological classification, valid in all dimensions, of the locally linear, orientation-reversing, involutions on tori with fixed point set of codimension one.

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 finite groups acting on acyclic complexes of dimension two.

Carles Casacuberta, Warren Dicks (1992)

Publicacions Matemàtiques

We conjecture that every finite group G acting on a contractible CW-complex X of dimension 2 has at least one fixed point. We prove this in the case where G is solvable, and under this additional hypothesis, the result holds for X acyclic.

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