3-manifolds that bound no definite 4-manifold
Geometric Topology
2021-01-08 v2
Abstract
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 cobordant to a Seifert fibered space or any 3-manifold obtained by Dehn surgery on a knot. The proof requires an analysis of short characteristic covectors in bimodular lattices.
Keywords
Cite
@article{arxiv.2012.12929,
title = {3-manifolds that bound no definite 4-manifold},
author = {Marco Golla and Kyle Larson},
journal= {arXiv preprint arXiv:2012.12929},
year = {2021}
}
Comments
Version 2: new result about bimodular lattices that simplifies the argument; minor changes elsewhere