Geometric obstructions for $ξ$-fillings of 3-manifolds

arXiv (Cornell University) 2026 Preprint Open access

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Authors: Daniel Galvin, Peter Teichner, Simona Veselá
DOI: 10.48550/arxiv.2601.09650
Cited by: 0

Abstract

We consider the realisation problem for normal 1-types of 4-manifolds with a given boundary. More precisely, given a normal 1-type $ξ$ and closed 3-dimensional $ξ$-manifold $Y$, does there exist a compact 4-dimensional $ξ$-manifold with boundary $Y$? 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.

Fields of Study & Subjects

Geometric and Algebraic Topology Homotopy and Cohomology in Algebraic Topology Algebraic Geometry and Number Theory

Publication details

Journal / source
arXiv (Cornell University)
Publication date
14 January 2026
Language
EN
Document type
Preprint