Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Obstructions to smooth group actions on 4-manifolds from families
  Seiberg-Witten theory   Let $X$ be a smooth, compact, oriented $4$-manifold. Building upon work of
Li-Liu, Ruberman, Nakamura and Konno, we consider a families version of
Seiberg-Witten theory and obtain obstructions to the existence of certain group
actions on $X$ by diffeomorphisms. The obstructions show that certain group
actions on $H^2(X , \mathbb{Z})$ preserving the intersection form can not be
lifted an action of the same group on $X$ by diffeomorphisms. Using our
obstructions, we construct numerous examples of group actions which can be
realised continuously but can not be realised smoothly for any differentiable
structure. For example, we construct compact simply-connected $4$-manifolds $X$
and involutions $f : H^2(X , \mathbb{Z}) \to H^2(X , \mathbb{Z})$ such that $f$
can be realised by a continuous involution on $X$ or by a diffeomorphism, but
not by an involutive diffeomorphism for any smooth structure on $X$.

9
The categories of this paper are: nlin
14
The categories of this paper are: math-ph
15
The categories of this paper are: nucl-ex
22
The categories of this paper are: chao-dyn
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The categories of this paper are: acc-phys
24
The categories of this paper are: dg-ga
32
The categories of this paper are: atom-ph
23
The categories of this paper are: solv-int
13
The categories of this paper are: quant-ph
27
The categories of this paper are: comp-gas
1
The categories of this paper are: cs
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The categories of this paper are: eess
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The categories of this paper are: hep-lat
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The categories of this paper are: cmp-lg
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The categories of this paper are: gr-qc
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The categories of this paper are: cond-mat