Maximal actions of finite 2-groups on ${\Bbb Z}_2$-homology 3-spheres

Volume 184 / 2004

Mattia Mecchia Fundamenta Mathematicae 184 (2004), 205-221 MSC: 57M60, 57M12. DOI: 10.4064/fm184-0-13

Abstract

It is known that a finite 2-group acting on a ${{\mathbb Z}}_2$-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.

Authors

  • Mattia MecchiaDipartimento di Scienze Matematiche
    Università degli Studi di Trieste
    Via A. Valerio 12/1
    34127 Trieste, Italy
    e-mail

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