scholarly journals Graph manifolds, left-orderability and amalgamation

2013 ◽  
Vol 13 (4) ◽  
pp. 2347-2368 ◽  
Author(s):  
Adam Clay ◽  
Tye Lidman ◽  
Liam Watson
Keyword(s):  
Graph Manifolds

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

Mathematics ◽  
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.

scholarly journals Graph manifolds with boundary are virtually special

2013 ◽  
Vol 7 (2) ◽  
pp. 419-435 ◽  
Author(s):  
Piotr Przytycki ◽  
Daniel T. Wise
Keyword(s):  
Manifolds With Boundary ◽  
Graph Manifolds

scholarly journals Integral approximation of simplicial volume of graph manifolds

2019 ◽  
Vol 51 (4) ◽  
pp. 715-731 ◽  
Author(s):  
Daniel Fauser ◽  
Stefan Friedl ◽  
Clara Löh
Keyword(s):  
Simplicial Volume ◽  
Integral Approximation ◽  
Graph Manifolds

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

2018 ◽  
Vol 61 (1) ◽  
pp. 211-224 ◽  
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.

scholarly journals L-spaces, taut foliations, and graph manifolds

2020 ◽  
Vol 156 (3) ◽  
pp. 604-612 ◽  
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.

scholarly journals Topological Realizations of Line Arrangements

2017 ◽  
Vol 2019 (8) ◽  
pp. 2295-2331
Author(s):  
Daniel Ruberman ◽  
Laura Starkston
Keyword(s):  
Finite Field ◽  
Projective Plane ◽  
Contact Structure ◽  
Complex Projective Plane ◽  
Real Projective Plane ◽  
Incidence Relation ◽  
Combinatorial Configuration ◽  
Important Variation ◽  
Graph Manifolds ◽  
Complex Projective

Abstract A venerable problem in combinatorics and geometry asks whether a given incidence relation may be realized by a configuration of points and lines. The classic version of this would ask for lines in a projective plane over a field. An important variation allows for pseudolines: embedded circles (isotopic to $\mathbb R\rm{P}^1$) in the real projective plane. In this article we investigate whether a configuration is realized by a collection of 2-spheres embedded, in symplectic, smooth, and topological categories, in the complex projective plane. We find obstructions to the existence of topologically locally flat spheres realizing a configuration, and show for instance that the combinatorial configuration corresponding to the projective plane over any finite field is not realized. Such obstructions are used to show that a particular contact structure on certain graph manifolds is not (strongly) symplectically fillable. We also show that a configuration of real pseudolines can be complexified to give a configuration of smooth, indeed symplectically embedded, 2-spheres.

scholarly journals Profinite properties of graph manifolds

2009 ◽  
Vol 147 (1) ◽  
pp. 29-45 ◽  
Author(s):  
Henry Wilton ◽  
Pavel Zalesskii
Keyword(s):  
Graph Manifolds

scholarly journals Cocompactly cubulated graph manifolds

2015 ◽  
Vol 207 (1) ◽  
pp. 377-394 ◽  
Author(s):  
Mark F. Hagen ◽  
Piotr Przytycki
Keyword(s):  
Graph Manifolds
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