On Manolescu's $\kappa$-invariants of rational homology 3-spheres

TL;DR

This paper provides estimates and methods to determine Manolescu's ppa-invariant for rational homology 3-spheres using spin 4-orbifolds, with applications to Dehn surgeries on knots in S^3.

Contribution

It introduces a new approach to estimate and sometimes exactly compute the ppa-invariant using 4-orbifold data, especially in the context of Dehn surgeries.

Findings

Estimates for ppa-invariant based on spin 4-orbifold data

Examples of ppa-invariant determination via specific 4-orbifolds

Application to Dehn surgeries along knots in S^3

Abstract

We give an estimate for Manolescu's $\kappa$-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 $\kappa$. We give such examples in case of Dehn surgeries along knots in $S^3$.