Finite Group Actions on Kervaire Manifolds
نویسندگان
چکیده
Let M K be the Kervaire manifold: a closed, piecewise linear (PL) manifold with Kervaire invariant 1 and the same homology as the product S × S of spheres. We show that a finite group of odd order acts freely on M K if and only if it acts freely on S × S. If MK is smoothable, then each smooth structure on MK admits a free smooth involution. If k 6= 2 − 1, then M K does not admit any free TOP involutions. Free “exotic” (PL) involutions are constructed on M K , M K , and M K . Each smooth structure on M K admits a free Z/2× Z/2 action.
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تاریخ انتشار 2013