Handlebody Neighbourhoods and a conjecture of Adjamagbo
David Gauld

TL;DR
This paper proves a conjecture by Adjamagbo using handlebodies, showing that certain submanifolds can be extended to a nested family covering the entire manifold with specific boundary properties.
Contribution
It introduces a handlebody-based method to verify a conjecture about submanifold frontiers and nested neighborhoods in manifolds.
Findings
Verified Adjamagbo's conjecture for manifolds with handlebody techniques.
Constructed an increasing family of open sets with submanifold frontiers.
Established a neighborhood basis for the manifold's closure.
Abstract
Using handlebodies we verify a conjecture of P Adjamagbo that if the frontier of a relatively compact subset of a manifold is a submanifold then there is an increasing family of relatively compact open sets indexed by the positive reals so that the frontier of each is a submanifold, their union is the whole manifold and for each the subfamily indexed by is a neighbourhood basis of the closure of the set.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · graph theory and CDMA systems · Advanced Mathematical Theories
