L-spaces, taut foliations, and graph manifolds

Jonathan Hanselman; Jacob Rasmussen; Sarah Dean Rasmussen; Liam Watson

doi:10.1112/s0010437x19007814

L-spaces, taut foliations, and graph manifolds

Compositio Mathematica ◽

10.1112/s0010437x19007814 ◽

2020 ◽

Vol 156 (3) ◽

pp. 604-612 ◽

Cited By ~ 3

Author(s):

Jonathan Hanselman ◽

Jacob Rasmussen ◽

Sarah Dean Rasmussen ◽

Liam Watson

Keyword(s):

Graph Manifold ◽

Graph Manifolds

If $Y$ is a closed orientable graph manifold, we show that $Y$ admits a coorientable taut foliation if and only if $Y$ is not an L-space. Combined with previous work of Boyer and Clay, this implies that $Y$ is an L-space if and only if $\unicode[STIX]{x1D70B}_{1}(Y)$ is not left-orderable.

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Conjugacy Problem in the Fundamental Groups of High-Dimensional Graph Manifolds

Mathematics ◽

10.3390/math9121330 ◽

2021 ◽

Vol 9 (12) ◽

pp. 1330

Author(s):

Raeyong Kim

Keyword(s):

Group Structure ◽

Conjugacy Problem ◽

High Dimensional ◽

Fundamental Groups ◽

Graph Manifold ◽

Solvable Word Problem ◽

Algorithmic Problems ◽

Graph Manifolds ◽

Dimensional Graph ◽

Solvable Word

The conjugacy problem for a group G is one of the important algorithmic problems deciding whether or not two elements in G are conjugate to each other. In this paper, we analyze the graph of group structure for the fundamental group of a high-dimensional graph manifold and study the conjugacy problem. We also provide a new proof for the solvable word problem.

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The Asymptotics of the Higher Dimensional Reidemeister Torsion for Exceptional Surgeries Along Twist Knots

Canadian Mathematical Bulletin ◽

10.4153/cmb-2017-021-5 ◽

2018 ◽

Vol 61 (1) ◽

pp. 211-224 ◽

Cited By ~ 1

Author(s):

Anh T. Tran ◽

Yoshikazu Yamaguchi

Keyword(s):

Asymptotic Behavior ◽

Reidemeister Torsion ◽

Graph Manifold ◽

Higher Dimensional ◽

Graph Manifolds

AbstractWe determine the asymptotic behavior of the higher dimensional Reidemeister torsion for the graph manifolds obtained by exceptional surgeries along twist knots. We show that all irreducible SL2()-representations of the graph manifold are induced by irreducible metabelian representations of the twist knot group. We also give the set of the limits of the leading coeõcients in the higher dimensional Reidemeister torsion explicitly.

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L-space intervals for graph manifolds and cables

Compositio Mathematica ◽

10.1112/s0010437x16008319 ◽

2017 ◽

Vol 153 (5) ◽

pp. 1008-1049 ◽

Cited By ~ 6

Author(s):

Sarah Dean Rasmussen

Keyword(s):

Recursive Formula ◽

Dehn Filling ◽

Graph Manifold ◽

Seifert Fibered Spaces ◽

Graph Manifolds ◽

Special Case ◽

Space Interval

We present a graph manifold analog of the Jankins–Neumann classification of Seifert fibered spaces over$S^{2}$admitting taut foliations, providing a finite recursive formula to compute the L-space Dehn-filling interval for any graph manifold with torus boundary. As an application of a generalization of this result to Floer simple manifolds, we compute the L-space interval for any cable of a Floer simple knot complement in a closed three-manifold in terms of the original L-space interval, recovering a result of Hedden and Hom as a special case.

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Classification and rigidity of totally periodic pseudo-Anosov flows in graph manifolds

Ergodic Theory and Dynamical Systems ◽

10.1017/etds.2014.9 ◽

2014 ◽

Vol 35 (6) ◽

pp. 1681-1722 ◽

Cited By ~ 2

Author(s):

THIERRY BARBOT ◽

SÉRGIO R. FENLEY

Keyword(s):

Homotopy Class ◽

Closed Orbit ◽

Dehn Surgery ◽

Anosov Flow ◽

Free Homotopy Class ◽

Graph Manifold ◽

Finite Power ◽

Graph Manifolds ◽

Anosov Flows ◽

Regular Fibers

In this article we analyze totally periodic pseudo-Anosov flows in graph 3-manifolds. This means that in each Seifert fibered piece of the torus decomposition, the free homotopy class of regular fibers has a finite power which is also a finite power of the free homotopy class of a closed orbit of the flow. We show that each such flow is topologically equivalent to one of the model pseudo-Anosov flows which we previously constructed in Barbot and Fenley (Pseudo-Anosov flows in toroidal manifolds.Geom. Topol. 17(2013), 1877–1954). A model pseudo-Anosov flow is obtained by glueing standard neighborhoods of Birkhoff annuli and perhaps doing Dehn surgery on certain orbits. We also show that two model flows on the same graph manifold are isotopically equivalent (i.e. there is a isotopy of$M$mapping the oriented orbits of the first flow to the oriented orbits of the second flow) if and only if they have the same topological and dynamical data in the collection of standard neighborhoods of the Birkhoff annuli.

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Essential Surfaces in Graph Link Exteriors

Canadian Mathematical Bulletin ◽

10.4153/cmb-2009-028-9 ◽

2009 ◽

Vol 52 (2) ◽

pp. 257-266 ◽

Cited By ~ 3

Author(s):

Toru Ikeda

Keyword(s):

Euler Characteristic ◽

Seifert Manifold ◽

Essential Surface ◽

Graph Manifold ◽

Seifert Manifolds ◽

Essential Surfaces ◽

Graph Manifolds ◽

The Difference ◽

Two Sides ◽

Graph Link

AbstractAn irreducible graph manifold M contains an essential torus if it is not a special Seifert manifold. WhetherM contains a closed essential surface of negative Euler characteristic or not depends on the difference of Seifert fibrations from the two sides of a torus system which splits M into Seifert manifolds. However, it is not easy to characterize geometrically the class of irreducible graph manifolds which contain such surfaces. This article studies this problem in the case of graph link exteriors.

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Quasi-isometries of pairs: Surfaces in graph manifolds

International Journal of Algebra and Computation ◽

10.1142/s0218196719500218 ◽

2019 ◽

Vol 29 (04) ◽

pp. 681-698

Author(s):

Hoang Thanh Nguyen

Keyword(s):

Hausdorff Distance ◽

Closed Graph ◽

Graph Manifold ◽

Graph Manifolds

We show there exists a closed graph manifold [Formula: see text] and infinitely many non-separable, horizontal surfaces [Formula: see text] such that there does not exist a quasi-isometry [Formula: see text] taking [Formula: see text] to [Formula: see text] within a finite Hausdorff distance when [Formula: see text].

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