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Separability of embedded surfaces in 3-manifolds

Part of: Structure and classification of infinite or finite groups Low-dimensional topology

Published online by Cambridge University Press:  27 August 2014

Piotr Przytycki  and
Daniel T. Wise
Piotr Przytycki
Affiliation:
Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, 00-956 Warsaw, Poland email pprzytyc@mimuw.edu.pl
Daniel T. Wise
Affiliation:
Department of Mathematics and Statistics, McGill University, Montreal, QC, Canada H3A 0B9 email wise@math.mcgill.ca
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Abstract

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We prove that if $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}S$ is a properly embedded $\pi _1$-injective surface in a compact 3-manifold $M$, then $\pi _1S$ is separable in $\pi _1M$.

Keywords

3-manifoldsurfaceseparable

MSC classification

Secondary: 57M99: None of the above, but in this section 20E26: Residual properties and generalizations; residually finite groups
Type
Research Article
Information
Compositio Mathematica , Volume 150 , Issue 9 , September 2014 , pp. 1623 - 1630
Copyright
© The Author(s) 2014 

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