Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Gluing theorems for complete anti-self-dual spaces   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 K\"ahler 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 K\"ahler metrics that are asymptotic to the
Euclidean metric at infinity. A number of vanishing theorems for the
obstruction space is also included.

15
The categories of this paper are: nucl-ex
4
The categories of this paper are: cond-mat
7
The categories of this paper are: hep-th
34
The categories of this paper are: chem-ph
29
The categories of this paper are: funct-an
11
The categories of this paper are: hep-lat
27
The categories of this paper are: comp-gas
19
The categories of this paper are: eess
17
The categories of this paper are: q-fin
28
The categories of this paper are: alg-geom
36
The categories of this paper are: cmp-lg
23
The categories of this paper are: solv-int
37
The categories of this paper are: supr-con
32
The categories of this paper are: atom-ph
5
The categories of this paper are: gr-qc
6
The categories of this paper are: astro-ph