2009/08/24 by Daniel Cibotaru, Daniel F. Cibotaru, Cibotaru, Daniel F. +2
Mathematics · #35B25 #53B20 #58J20 #58J28 #58J30 #58J32 #Advanced Operator Algebra Research #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Functional Analysis (math.FA) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #math.AP #math.DG #math.FA #msc:35B25 #msc:53B20 #msc:58J20 #msc:58J28 #msc:58J30 #msc:58J32
paper · pdf · doi:10.48550/arxiv.0908.3236
31 pages, 3 figures; completely rewrote Section 4 using the definition of Kirk and Lesch of the Kashiwara-Wall index
openalex publication_date 2009/08/24 · arxiv created 2009/09/14 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We investigate the Dolbeault operator on a pair of pants, i.e., an elementary cobordism between a circle and the disjoint union of two circles. This operator induces a canonical selfadjoint Dirac operator Dt on each regular level set Ct of a fixed Morse function defining this cobordism. We show that as we approach the critical level set C0 from above and from below these operators converge in the gap topology to (different) selfadjoint operators D_± that we describe explicitly. We also relate the Atiyah-Patodi-Singer index of the Dolbeault operator on the cobordism to the spectral flows of the operators Dt on the complement of C0 and the Kashiwara-Wall index of a triplet of finite dimensional lagrangian spaces canonically determined by C0.