Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A gluing formula for families Seiberg-Witten invariants   We prove a gluing formula for the families Seiberg-Witten invariants of
families of $4$-manifolds obtained by fibrewise connected sum. Our formula
expresses the families Seiberg-Witten invariants of such a connected sum family
in terms of the ordinary Seiberg-Witten invariants of one of the summands,
under certain assumptions on the families. We construct some variants of the
families Seiberg-Witten invariants and prove the gluing formula also for these
variants. One variant incorporates a twist of the families moduli space using
the charge conjugation symmetry of the Seiberg-Witten equations. The other
variant is an equivariant Seiberg-Witten invariant of smooth group actions. We
consider several applications of the gluing formula including: obstructions to
smooth isotopy of diffeomorpihsms, computation of the mod $2$ Seiberg-Witten
invariants of spin structures, relations between mod $2$ Seiberg-Witten
invariants of $4$-manifolds and obstructions to the existence of invariant
metrics of positive scalar curvature for smooth group actions on $4$-manifolds.

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The categories of this paper are: hep-th
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The categories of this paper are: bayes-an
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The categories of this paper are: eess
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-ex
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The categories of this paper are: stat
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The categories of this paper are: cmp-lg
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The categories of this paper are: adap-org
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The categories of this paper are: solv-int
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The categories of this paper are: comp-gas
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The categories of this paper are: q-fin
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The categories of this paper are: nucl-ex
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The categories of this paper are: econ
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The categories of this paper are: cs
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The categories of this paper are: dg-ga
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The categories of this paper are: cond-mat