• Title, Summary, Keyword: handlebody decomposition

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GEOMETRIC RANK AND THE TUCKER PROPERTY

  • Otera, Daniele Ettore
    • Journal of the Korean Mathematical Society
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    • v.54 no.3
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    • pp.807-820
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    • 2017
  • An open smooth manifold is said of finite geometric rank if it admits a handlebody decomposition with a finite number of 1-handles. We prove that, if there exists a proper submanifold $W^{n+3}$ of finite geometric rank between an open 3-manifold $V^3$ and its stabilization $V^3{\times}B^n$(where $B^n$ denotes the standard n-ball), then the manifold $V^3$ has the Tucker property. This means that for any compact submanifold $C{\subset}V^3$, the fundamental group ${\pi}_1(V^3-C)$ is finitely generated. In the irreducible case this implies that $V^3$ has a well-behaved compactification.