The Geometry of b^k Manifolds

2013/04/13 by Geoffrey Scott, Scott, Geoffrey
Mathematics · #53D05 #FOS: Mathematics #Symplectic Geometry (math.SG) #math.SG #msc:53D05

paper · pdf · doi:10.48550/arxiv.1304.3821

23 pages, 1 figure; added information about supporting grant in latest version

arxiv created 2013/07/30 · arxiv updated 2013/07/31

Abstract

Let Z be a hypersurface of a manifold M. The b-tangent bundle of (M, Z), whose sections are vector fields tangent to Z, is used to study pseudodifferential operators and stable Poisson structures on M. In this paper we introduce the b^k-tangent bundle, whose sections are vector fields with "order k tangency" to Z. We describe the geometry of this bundle and its dual, generalize the celebrated Mazzeo-Melrose theorem of the de Rham theory of b-manifolds, and apply these tools to classify certain Poisson structures on compact oriented surfaces.

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