Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The collapsing geometry of almost Ricci-flat 4-manifolds   We consider Riemannian 4-manifolds that Gromov-Hausdorff converge to a lower
dimensional limit space, with the Ricci tensor going to zero. Among other
things, we show that if the limit space is two dimensional then under some mild
assumptions, the limiting four dimensional geometry away from the curvature
blowup region is semiflat Kaehler.

21
The categories of this paper are: adap-org
13
The categories of this paper are: quant-ph
24
The categories of this paper are: dg-ga
28
The categories of this paper are: alg-geom
12
The categories of this paper are: nucl-th
17
The categories of this paper are: q-fin
18
The categories of this paper are: econ
27
The categories of this paper are: comp-gas
0
The categories of this paper are: hep-ph
25
The categories of this paper are: patt-sol
37
The categories of this paper are: supr-con
16
The categories of this paper are: stat
6
The categories of this paper are: astro-ph
26
The categories of this paper are: bayes-an
30
The categories of this paper are: q-alg
4
The categories of this paper are: cond-mat