Sums of lens spaces bounding rational balls

TL;DR

This paper classifies certain lens spaces that bound rational homology balls, determines their order in the cobordism group, and finds the concordance order of associated 2-bridge knots, advancing understanding of 3-manifold and knot invariants.

Contribution

It provides a classification of connected sums of lens spaces bounding rational homology balls and computes their orders in relevant cobordism and concordance groups.

Findings

Classified connected sums of lens spaces bounding rational homology balls.

Determined the order of each lens space in the rational homology cobordism group.

Established the concordance order of each 2-bridge knot.

Abstract

We classify connected sums of three-dimensional lens spaces which smoothly bound rational homology balls. We use this result to determine the order of each lens space in the group of rational homology 3-spheres up to rational homology cobordisms, and to determine the concordance order of each 2-bridge knot.