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Topology/Geometry Seminar
Wednesday, December 2, 2009
4 pm,
TBA
Courtney Thatcher
Lens Spaces and Free Z_p actions on Products of Spheres II.
Abstract: We consider free actions of large prime order cyclic groups on the product of any number of spheres of the same odd dimension and on products of two spheres of differing odd dimensions. We require only that the action be free on the product as a whole and not each sphere separately. In particular we determine
equivariant homotopy type, and for both linear actions and for even numbers of spheres the simple homotopy type and simple structure sets. The results are compared to the analysis and classification done for lens spaces.
Similar to lens spaces, the first k-invariant generally determines the homotopy type of many of the quotient spaces, however the Reidemeister torsion frequently vanishes and many of the homotopy equivalent spaces are also simple homotopy equivalent. Unlike lens spaces, which are determined by their k-invariant and Reidemeister torsion, the ½-invariant here often vanishes and the Pontrjagin classes become p-localized
homeomorphism invariants for a given dimension. The cohomology classes, Pontrjagin classes, and sets of normal invariants are computed in the process.
We meet weekly on Friday afternoons at Penn State Altoona (and sometimes at Penn State University Park). If you are interested in giving a talk in our seminar please contact one of the coordinators for the Spring 2009 semester: Wojtek Dorabiala and Aissa Wade.
