Embedded surfaces with infinite cyclic knot group
Abstract
We study locally flat, compact, oriented surfaces in -manifolds whose exteriors have infinite cyclic fundamental group. We give algebraic topological criteria for two such surfaces, with the same genus , to be related by an ambient homeomorphism, and further criteria that imply they are ambiently isotopic. Along the way, we prove that certain pairs of topological -manifolds with infinite cyclic fundamental group, homeomorphic boundaries, and equivalent equivariant intersection forms, are homeomorphic.
Cite
@article{arxiv.2009.13461,
title = {Embedded surfaces with infinite cyclic knot group},
author = {Anthony Conway and Mark Powell},
journal= {arXiv preprint arXiv:2009.13461},
year = {2026}
}
Comments
v2 fixes an error in the proof of Theorem 1.3. The issue in the proof Theorem 5.10 (now Theorem 5.11) has been corrected. v3, v4 are reorganisations; new figures and applications are added. v5: Added report number. v6: Fixed the definition of a trivial 1-handle stabilisation. To appear in Geometry & Topology. v7: Fixes an error: Theorems 1.7, 1.8 on n-roll 1-twist rim surgery only hold for n=0