Title : On finite nonsolvable groups acting on homology spheres
Speaker : Mattia Mecchia (Universita' degli studi di Trieste)
Abstract :

In knot theory, $\Bbb{Z}_2$-homology 3-spheres (i.e.manifolds with the $\Bbb{Z}_2$-homology of the 3-sphere) appear often: for example the manifolds obtained by $p/q$-surgery on knots in $S^3$, with $p$ odd, and the 2-fold branched coverings of knots are $\Bbb{Z}_2$-homology 3-spheres. We consider the problem to determine which finite groups admit an action on a $\Bbb{Z}_2$-homology 3-sphere; in particular our main result is a list of nonsolvable groups which are the candidates for such an action (obtained in joint work with B.Zimmermann). We present also some results about groups acting on homology 4-spheres.

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