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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm184-0-13,
author = {Mattia Mecchia},
title = {Maximal actions of finite 2-groups on Z2-homology 3-spheres},
journal = {Fundamenta Mathematicae},
volume = {184},
year = {2004},
pages = {205-221},
zbl = {1099.57014},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm184-0-13}
}
Mattia Mecchia. Maximal actions of finite 2-groups on ℤ₂-homology 3-spheres. Fundamenta Mathematicae, Tome 184 (2004) pp. 205-221. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm184-0-13/