Rational homology 3-spheres and simply connected definite bounding

Kouki Sato; Masaki Taniguchi

doi:10.2140/agt.2020.20.865

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arXiv · 1808.09135

Rational homology 3-spheres and simply connected definite bounding

Kouki Sato·Masaki Taniguchi

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Abstract

For each rational homology 3-sphere $Y$ which bounds simply connected definite 4-manifolds of both signs, we construct an infinite family of irreducible rational homology 3-spheres which are homology cobordant to $Y$ but cannot bound any simply connected definite 4-manifold. As a corollary, for any coprime integers $p,q$, we obtain an infinite family of irreducible rational homology 3-spheres which are homology cobordant to the lens space $L(p,q)$ but cannot obtained by a knot surgery.

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Kouki Sato, Masaki Taniguchi. 2018-08-28. Rational homology 3-spheres and simply connected definite bounding. https://doi.org/10.2140/agt.2020.20.865

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