# Complementary legs and rational balls

## TL;DR

This paper classifies Seifert rational homology spheres with two complementary legs that bound rational homology balls, linking the classification to the sliceness of certain Montesinos knots.

## Contribution

It provides a complete classification of Seifert manifolds with 3 exceptional fibers and two complementary legs that bound rational homology balls, connecting to knot sliceness.

## Key findings

- Classified Seifert manifolds with 3 exceptional fibers and complementary legs bounding rational homology balls.
- Established a relationship between these manifolds and the sliceness of specific Montesinos knots.
- Enhanced understanding of the topology of rational homology spheres and their bounding properties.

## Abstract

In this note we study the Seifert rational homology spheres with two complementary legs, i.e. with a pair of invariants whose fractions add up to one. We give a complete classification of the Seifert manifolds with 3 exceptional fibers and two complementary legs which bound rational homology balls. The result translates in a statement on the sliceness of some Montesinos knots.