Constructing Rational Homology 3-Spheres That Bound Rational Homology 4-Balls
Abstract
We present three large families of new examples of plumbed 3-manifolds that bound rational homology 4-balls. These are constructed using two operations, also defined here, that preserve the lack of a lattice embedding obstruction to bounding rational homology balls. Apart from in the cases shown in this paper, it remains open whether these operations are rational homology cobordisms in general. The families of new examples include a multitude of families of rational surgeries on torus knots, and we explicitly describe which positive torus knots we now know to have a surgery that bounds a rational homology ball. While not the focus of this paper, we implicitly confirm the slice-ribbon conjecture for new, more complicated, examples of arborescent knots, including many Montesinos knots.
Keywords
Cite
@article{arxiv.2208.14850,
title = {Constructing Rational Homology 3-Spheres That Bound Rational Homology 4-Balls},
author = {Lisa Lokteva},
journal= {arXiv preprint arXiv:2208.14850},
year = {2025}
}
Comments
39 pages, 35 figures. v3: The proof of the three families bounding rational homology balls was wrong in the first version, and restored only for two of the families in the second version. This version contains proofs for all three families. Moreover, this version has been updated for presentation