2009/08/31 by Ken Richardson, Richardson, Ken
Mathematics · #19L47. #58J70 #Advanced Operator Algebra Research #Advanced Topics in Algebra #Differential Geometry (math.DG) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #math.DG #msc:19L47. #msc:58J70
paper · pdf · doi:10.48550/arxiv.0908.4555
6 pages
arxiv created 2009/08/31 · openalex publication_date 2009/08/31 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This note surveys the well-known structure of G-manifolds and summarizes parts of two papers that have not yet appeared in print: one with joint with J. Bruning and F. W. Kamber, and another with I. Prokhorenkov. In particular, from a given manifold on which a compact Lie group acts smoothly, we construct a sequence of manifolds on which the same Lie group acts, but with fewer levels of singular strata. Global analysis and geometric results on the simpler manifolds may be translated to results on the original manifold. Further, we show that by utilizing bundles over a G-manifold with singular strata, we may construct natural equivariant transverse Dirac-type operators that have properties similar to Dirac operators on closed manifolds.