Cyclic branched coverings and homology 3-spheres with large group actions

Bruno P. Zimmermann

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Some results and conjectures on finite groups acting on homology spheres.

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Maximal actions of finite 2-groups on ℤ₂-homology 3-spheres

Mattia Mecchia (2004)

Fundamenta Mathematicae

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It is known that a finite 2-group acting on a ℤ₂-homology 3-sphere has at most ten conjugacy classes of involutions; the action of groups with the maximal number of conjugacy classes of involutions is strictly related to some questions concerning the representation of hyperbolic 3-manifolds as 2-fold branched coverings of knots. Using a low-dimensional approach we classify these maximal actions both from an algebraic and from a geometrical point of view.