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Invariants of translation surfaces

Pascal Hubert, Thomas A. Schmidt (2001)

Annales de l’institut Fourier

We definite invariants of translation surfaces which refine Veech groups. These aid in exact determination of Veech groups. We give examples where two surfaces of isomorphic Veech group cannot even share a common tree of balanced affine coverings. We also show that there exist translation surfaces of isomorphic Veech groups which cannot affinely cover any common surface. We also extend a result of Gutkin and Judge and thereby give the first examples of noncompact Fuchsian...

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.

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