Spherical 3-manifolds bounding rational homology balls

TL;DR

This paper classifies spherical 3-manifolds that bound rational homology 4-balls and determines their order in the cobordism group, using Donaldson's theorem and Heegaard Floer invariants.

Contribution

It provides a complete classification of spherical 3-manifolds bounding rational homology balls and computes their order in the cobordism group, advancing understanding of 3- and 4-manifold relations.

Findings

Complete classification of spherical 3-manifolds bounding rational homology 4-balls

Determination of the order of these manifolds in the cobordism group

Application of Donaldson's theorem and Heegaard Floer correction terms

Abstract

We give a complete classification of the spherical 3-manifolds that bound smooth rational homology 4-balls. Furthermore, we determine the order of spherical 3-manifolds in the rational homology cobordism group of rational homology 3-spheres. To this end, we use constraints for 3-manifolds to bound rational homology balls induced from Donaldson's diagonalization theorem and Heegaard Floer correction terms.