# GEOMETRIC RANK AND THE TUCKER PROPERTY

• Otera, Daniele Ettore (Mathematics and Informatics Institute Vilnius University)
• Published : 2017.05.01
• 38 15

#### Abstract

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.

#### Keywords

handlebody decomposition;singularities;triangulations;Tucker property

#### Acknowledgement

Supported by : Research Council of Lithuania

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