Embedded surfaces with infinite cyclic knot group

Anthony Conway; Mark Powell

doi:10.2140/gt.2023.27.739

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arXiv · 2009.13461

Embedded surfaces with infinite cyclic knot group

Anthony Conway·Mark Powell

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Abstract

We study locally flat, compact, oriented surfaces in $4$-manifolds whose exteriors have infinite cyclic fundamental group. We give algebraic topological criteria for two such surfaces, with the same genus $g$, 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 $4$-manifolds with infinite cyclic fundamental group, homeomorphic boundaries, and equivalent equivariant intersection forms, are homeomorphic.

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Anthony Conway, Mark Powell. 2020-09-28. Embedded surfaces with infinite cyclic knot group. https://doi.org/10.2140/gt.2023.27.739

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