Constructing rational homology 3-spheres that bound rational homology 4-balls

Lokteva, Lisa

doi:10.2140/agt.2025.25.4599

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ISSN (electronic): 1472-2739

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Constructing rational homology $3$-spheres that bound rational homology $4$-balls

Lisa Lokteva

Algebraic & Geometric Topology 25 (2025) 4599–4631

DOI: 10.2140/agt.2025.25.4599

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 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

rational homology balls, rational balls, rational surgeries on torus knots, plumbed 3-manifolds, rational fillings, lattice embeddings, complementary legs, graph manifolds, Lisca expansions, growth of complementary legs

Mathematical Subject Classification

Primary: 57K40, 57K41

References

Publication

Received: 8 September 2022

Revised: 3 May 2024

Accepted: 25 July 2024

Published: 20 November 2025

Authors

Lisa Lokteva
Ångströmlaboratoriet Uppsala Universitet Uppsala Sweden

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Volume 25, issue 8 (2025)