Homotopy complex projective spaces with Pin(2)-action

Details Homotopy complex projective spaces with Pin(2)-action Homotopy complex projective spaces with Pin(2)-action

2001-02-07

arxiv.org/abs/math/0102061v1

Mathematics

Geometric Topology

16 pages, no figures

Scientific paper

Let $M$ be a manifold homotopy equivalent to the complex projective space $\C P^m$. Petrie conjectured that $M$ has standard total Pontrjagin class if $M$ admits a non-trivial action by $S^1$. We prove the conjecture for $m<12$ under the assumption that the action extends to a nice $Pin(2)$-action with fixed point. The proof involves equivariant index theory for $Spin^c$-manifolds and Jacobi functions as well as classical results from the theory of transformation groups.

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