Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the blow-up of four dimensional Ricci flow singularities   In this paper we prove a conjecture by Feldman-Ilmanen-Knopf in \cite{FIK}
that the gradient shrinking soliton metric they constructed on the tautological
line bundle over $\CP^1$ is the uniform limit of blow-ups of a type I Ricci
flow singularity on a closed manifold. We use this result to show that limits
of blow-ups of Ricci flow singularities on closed four dimensional manifolds do
not necessarily have non-negative Ricci curvature.

17
The categories of this paper are: q-fin
4
The categories of this paper are: cond-mat
14
The categories of this paper are: math-ph
22
The categories of this paper are: chao-dyn
15
The categories of this paper are: nucl-ex
5
The categories of this paper are: gr-qc
16
The categories of this paper are: stat
7
The categories of this paper are: hep-th
13
The categories of this paper are: quant-ph
11
The categories of this paper are: hep-lat
12
The categories of this paper are: nucl-th
8
The categories of this paper are: hep-ex
32
The categories of this paper are: atom-ph
10
The categories of this paper are: q-bio
18
The categories of this paper are: econ
33
The categories of this paper are: plasm-ph