Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Gap Theorem for Half-Conformally Flat Manifolds   We show that any compact half-conformally flat manifold of negative type,
with bounded $L^2$ energy, sufficiently small scalar curvature, and a
non-collapsing assumption, has all betti numbers bounded. We show that this
result is optimal from an analytic perspective by demonstrating singularity
models that are 2-ended, and are asymptotically K\"ahler on both ends. We show
that bounded self-dual solutions of $d\omega=0$ on ALE manifold ends are either
asymptotically K\"ahler, or they have a decay rate of $O(r^{-4})$ or better.

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The categories of this paper are: cs
9
The categories of this paper are: nlin
34
The categories of this paper are: chem-ph
28
The categories of this paper are: alg-geom
8
The categories of this paper are: hep-ex
12
The categories of this paper are: nucl-th
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The categories of this paper are: eess
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The categories of this paper are: q-fin
0
The categories of this paper are: hep-ph
30
The categories of this paper are: q-alg
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The categories of this paper are: cond-mat
5
The categories of this paper are: gr-qc
35
The categories of this paper are: mtrl-th
33
The categories of this paper are: plasm-ph
29
The categories of this paper are: funct-an
24
The categories of this paper are: dg-ga