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Brieskorn varietes and fake lens spaces

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Jim Davis
Indiana U/MPI
Mon, 26/04/2010 - 15:00 - 16:00
MPIM Lecture Hall
Parent event: 
Topics in Topology

Brieskorn varietes admit $S^1$-actions whose isotropy groups are finite. Choose a Brieskorn variety diffeomorphic to a sphere and an odd prime p which is relatively prime to the order of all isotropy groups. Then the orbit space of the induced $Z/p$-action is a homotopy lens space -- a closed manifold homotopy equivalent to a lens space. A homotopy lens space is fake if it is not homeomorphic to a classical lens space. Using Reidemeister torsion, we show some of these homotopy lens spaces are fake lens spaces.

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