Surgeries on Iterated Torus Knots Bounding Rational Homology 4-Balls

Lisa Lokteva

Surgeries on Iterated Torus Knots Bounding Rational Homology 4-Balls

Geometric Topology 2023-06-21 v2

Authors: Lisa Lokteva

Abstract

We show that all large enough positive integral surgeries on algebraic knots bound a 4-manifold with a negative definite plumbing tree, which we describe explicitly. Then we apply the lattice embedding obstruction coming from Donaldson's Theorem to classify the ones of the form $S^3_n(T(p_1,k_1p_1+1; p_2, k_2p_2\pm 1))$ that also bound rational homology 4-balls.

Keywords

iterated torus knots rational homology 4-balls surgery algebraic knots plumbing tree donaldson theorem lattice embedding obstruction

Cite

@article{arxiv.2110.05459,
  title  = {Surgeries on Iterated Torus Knots Bounding Rational Homology 4-Balls},
  author = {Lisa Lokteva},
  journal= {arXiv preprint arXiv:2110.05459},
  year   = {2023}
}

Comments

26 pages, 18 figures (including subfigures). To appear in Proceedings of the Edinburgh Mathematical Society

Surgeries on Iterated Torus Knots Bounding Rational Homology 4-Balls

Abstract

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