Geometric obstructions for $\xi$-fillings of 3-manifolds
Geometric Topology
2026-01-15 v1 Algebraic Topology
Abstract
We consider the realisation problem for normal 1-types of 4-manifolds with a given boundary. More precisely, given a normal 1-type and closed 3-dimensional -manifold , does there exist a compact 4-dimensional -manifold with boundary ? We describe a three stage obstruction theory for the existence of such a 4-manifold, with our main contribution being a `tertiary' obstruction that we describe geometrically via Wall's quadratic self-intersection form.
Keywords
Cite
@article{arxiv.2601.09650,
title = {Geometric obstructions for $\xi$-fillings of 3-manifolds},
author = {Daniel Galvin and Peter Teichner and Simona Veselá},
journal= {arXiv preprint arXiv:2601.09650},
year = {2026}
}
Comments
Comments welcome!