1998/03/31 by Liviu I. Nicolaescu, Nicolaescu, Liviu I. · 1 citation
Computer Science · Mathematics · #58G03 #58G18 #Advanced Mathematical Modeling in Engineering #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations #math.DG #msc:58G03 #msc:58G18
paper · pdf · doi:10.48550/arxiv.math/9803154
Latex 2.09 with macro sec.sty (included), 26 pages, 1 figure
arxiv created 1998/03/31 · openalex publication_date 1998/03/31 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We formulate a more conceptual interpretation of the Cappell-Lee-Miller glueing/splitting theorem using the new language of asymptotic maps and asymptotic exactness. Additionally, we present an asymptotic description of the Mayer-Vietoris sequence naturally associated to the Cech cohomology of the sheaf of local solutions of a Dirac type operator. We discuss applications to eigenvalue estimates, approximation of obstruction bundles and glueing of determinant line bundles frequently arising in gauge theoretic problems. The operators involved in all these results need not be translation invariant.