For each rational homology –sphere which bounds simply connected definite –manifolds of both signs, we construct an infinite family of irreducible rational homology –spheres which are homology cobordant to but cannot bound any simply connected definite –manifold. As a corollary, for any coprime integers and , we obtain an infinite family of irreducible rational homology –spheres which are homology cobordant to the lens space but cannot be obtained by a knot surgery.
"Rational homology $3$–spheres and simply connected definite bounding." Algebr. Geom. Topol. 20 (2) 865 - 882, 2020. https://doi.org/10.2140/agt.2020.20.865