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2017 Affine Hirsch foliations on $3$–manifolds
Bin Yu
Algebr. Geom. Topol. 17(3): 1743-1770 (2017). DOI: 10.2140/agt.2017.17.1743

Abstract

This paper is devoted to discussing affine Hirsch foliations on 3–manifolds. First, we prove that up to isotopic leaf-conjugacy, every closed orientable 3–manifold M admits zero, one or two affine Hirsch foliations. Furthermore, every case is possible.

Then we analyze the 3–manifolds admitting two affine Hirsch foliations (we call these Hirsch manifolds). On the one hand, we construct Hirsch manifolds by using exchangeable braided links (we call such Hirsch manifolds DEBL Hirsch manifolds); on the other hand, we show that every Hirsch manifold virtually is a DEBL Hirsch manifold.

Finally, we show that for every n , there are only finitely many Hirsch manifolds with strand number n. Here the strand number of a Hirsch manifold M is a positive integer defined by using strand numbers of braids.

Citation

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Bin Yu. "Affine Hirsch foliations on $3$–manifolds." Algebr. Geom. Topol. 17 (3) 1743 - 1770, 2017. https://doi.org/10.2140/agt.2017.17.1743

Information

Received: 16 April 2016; Revised: 12 October 2016; Accepted: 18 December 2016; Published: 2017
First available in Project Euclid: 16 November 2017

zbMATH: 1376.57018
MathSciNet: MR3677938
Digital Object Identifier: 10.2140/agt.2017.17.1743

Subjects:
Primary: 57M50, 57R32
Secondary: 37E10, 57M25

Rights: Copyright © 2017 Mathematical Sciences Publishers

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Vol.17 • No. 3 • 2017
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