Homotopy complex projective spaces with Pin(2)-action

2001/02/07 by Anand Dessai, Dessai, Anand
Mathematics · #19J35 #19L47 #57R20 #57S25 #Advanced Algebra and Geometry #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Geometric Topology (math.GT) #Homotopy and Cohomology in Algebraic Topology #math.AT #math.GT #msc:19J35 #msc:19L47 #msc:57R20 #msc:57S25

paper · pdf · doi:10.48550/arxiv.math/0102061

16 pages, no figures

arxiv created 2001/02/07 · openalex publication_date 2001/02/07 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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 S¹. 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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