We give an estimate for Manolescu's κ-invariant of a rational homology 3-sphere Y by the data of a spin 4-orbifold bounded by Y. By an appropriate choice of a 4-orbifold, sometimes we can restrict and determine the value of κ. We give such examples in case of Dehn surgeries along knots in S³.
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Masaaki Ue (2024) studied this question.
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