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Journal Article

Embedded surfaces with infinite cyclic knot group

MPS-Authors
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Conway,  Anthony
Max Planck Institute for Mathematics, Max Planck Society;

/persons/resource/persons236018

Powell,  Mark
Max Planck Institute for Mathematics, Max Planck Society;

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2009.13461.pdf
(Preprint), 2MB

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Citation

Conway, A., & Powell, M. (in press). Embedded surfaces with infinite cyclic knot group. Geometry and Topology, To appear.


Cite as: https://hdl.handle.net/21.11116/0000-000A-0020-1
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.