Gluing theorems for complete anti-self-dual spaces
| dc.creator | Kovalev, A. G. | |
| dc.creator | Singer, M. A. | |
| dc.date | 2000-09-15 | |
| dc.date.accessioned | 2026-07-07T04:37:26Z | |
| dc.date.available | 2026-07-07T04:37:26Z | |
| dc.description | We give new and rather general gluing theorems for anti-self-dual (ASD) conformal structures, following the method suggested by Floer. The main result is a gluing theorem for pairs of conformally ASD manifolds `joined' across a common piece (union of connected components) of their boundaries. This theorem genuinely operates in the b-category (in the sense of Melrose) and in general the boundary of the joined manifold can be non-empty. The resulting metric is a conformally ASD b-metric or, in more traditional language, a complete conformally ASD metric with cylindrical asymptotics. We also study hermitian-ASD conformal structures on complex surfaces in relation to scalar-flat Kähler geometry. The general results are illustrated with a simple application, showing that the blow-up of C^2 at an arbitrary finite set of points admits scalar-flat Kähler metrics that are asymptotic to the Euclidean metric at infinity. A number of vanishing theorems for the obstruction space is also included. | |
| dc.description | 39 pages, 1 Postscript figure | |
| dc.identifier | https://arxiv.org/abs/math/0009158 | |
| dc.identifier | http://arxiv.org/abs/math/0009158 | |
| dc.identifier | Geom. Funct. Anal. 11 (2001), 1229--1281 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/59947 | |
| dc.subject | Differential Geometry | |
| dc.subject | 53C21 (Primary); 58J10, 53A30, 53C55, 53C25 (Secondary) | |
| dc.title | Gluing theorems for complete anti-self-dual spaces | |
| dc.type | text |