Constructing Rational Homology 3-Spheres That Bound Rational Homology 4-Balls

Lisa Lokteva

doi:10.2140/agt.2025.25.4599

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arXiv · 2208.14850

Constructing Rational Homology 3-Spheres That Bound Rational Homology 4-Balls

Lisa Lokteva

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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.

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Lisa Lokteva. 2022-08-31. Constructing Rational Homology 3-Spheres That Bound Rational Homology 4-Balls. https://doi.org/10.2140/agt.2025.25.4599

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