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math.GT2021
3-manifolds that bound no definite 4-manifold
Marco Golla, Kyle Larson
We produce a rational homology 3-sphere that does not smoothly bound either a positive or negative definite 4-manifold. Such a 3-manifold necessarily cannot be rational homology co…
math.GT2020★ 5 cited
Surgeries on torus knots, rational balls, and cabling
Paolo Aceto, Marco Golla, Kyle Larson +1
We classify which positive integral surgeries on positive torus knots bound rational homology balls. Additionally, for a given knot K we consider which cables K(p,q) admit integral…
math.GT2018
Lattices and correction terms
Kyle Larson
Let L be a nonunimodular definite lattice. Using a theorem of Elkies we show that whether L embeds in the standard definite lattice of the same rank is completely determined by a c…