Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On finite symmetries of simply connected four-manifolds   For most positive integer pairs $(a,b)$, the topological space $#a{\mathbb C
\mathbb P}^2#b{\bar{\mathbb C \mathbb P^2}}$ is shown to admit infinitely many
inequivalent smooth structures which dissolve upon performing a single
connected sum with $S^2\times S^2$. This is then used to construct infinitely
many non-equivalent smooth free actions of suitable finite groups on the
connected sum $#a{\mathbb C \mathbb P}^2#b{\bar{\mathbb C \mathbb P^2}}$. We
then investigate the behavior of the sign of the Yamabe invariant for the
resulting finite covers, and observe that these constructions provide many new
counter-examples to the $4$-dimensional Rosenberg Conjecture.

30
The categories of this paper are: q-alg
18
The categories of this paper are: econ
12
The categories of this paper are: nucl-th
8
The categories of this paper are: hep-ex
1
The categories of this paper are: cs
9
The categories of this paper are: nlin
28
The categories of this paper are: alg-geom
11
The categories of this paper are: hep-lat
23
The categories of this paper are: solv-int
33
The categories of this paper are: plasm-ph
17
The categories of this paper are: q-fin
37
The categories of this paper are: supr-con
13
The categories of this paper are: quant-ph
5
The categories of this paper are: gr-qc
27
The categories of this paper are: comp-gas
7
The categories of this paper are: hep-th