Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Negative Sasakian structures on simply-connected 5-manifolds   We study several questions on the existence of negative Sasakian structures
on simply connected rational homology spheres and on Smale-Barden manifolds of
the form $\#_k(S^2\times S^3)$. First, we prove that any simply connected
rational homology sphere admitting positive Sasakian structures also admits a
negative one. This result answers the question, posed by Boyer and Galicki in
their book [BG], of determining which simply connected rational homology
spheres admit both negative and positive Sasakian structures. Second, we prove
that the connected sum $\#_k(S^2\times S^3)$ admits negative quasi-regular
Sasakian structures for any $k$. This yields a complete answer to another
question posed in [BG].

30
The categories of this paper are: q-alg
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The categories of this paper are: alg-geom
33
The categories of this paper are: plasm-ph
8
The categories of this paper are: hep-ex
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The categories of this paper are: cmp-lg
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The categories of this paper are: eess
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The categories of this paper are: dg-ga
12
The categories of this paper are: nucl-th
14
The categories of this paper are: math-ph
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The categories of this paper are: econ
4
The categories of this paper are: cond-mat
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The categories of this paper are: comp-gas
15
The categories of this paper are: nucl-ex
32
The categories of this paper are: atom-ph
23
The categories of this paper are: solv-int
1
The categories of this paper are: cs