scholarly journals Profinite rigidity of graph manifolds and JSJ decompositions of 3-manifolds

2018 ◽  
Vol 502 ◽  
pp. 538-587 ◽  
Author(s):  
Gareth Wilkes
Keyword(s):  
Graph Manifolds ◽  
Jsj Decompositions

A CATALOGUE OF ORIENTABLE 3-MANIFOLDS TRIANGULATED BY 30 COLORED TETRAHEDRA

2008 ◽  
Vol 17 (05) ◽  
pp. 579-599 ◽  
Author(s):  
MARIA RITA CASALI ◽  
PAOLA CRISTOFORI
Keyword(s):  
Automatic Generation ◽  
Computational Approach ◽  
Equivalence Classes ◽  
Colored Graphs ◽  
One To One ◽  
Genus Two ◽  
Jsj Decompositions

The present paper follows the computational approach to 3-manifold classification via edge-colored graphs, already performed in [1] (with respect to orientable 3-manifolds up to 28 colored tetrahedra), in [2] (with respect to non-orientable 3-manifolds up to 26 colored tetrahedra), in [3] and [4] (with respect to genus two 3-manifolds up to 34 colored tetrahedra): in fact, by automatic generation and analysis of suitable edge-colored graphs, called crystallizations, we obtain a catalogue of all orientable 3-manifolds admitting colored triangulations with 30 tetrahedra. These manifolds are unambiguously identified via JSJ decompositions and fibering structures. It is worth noting that, in the present work, a suitable use of elementary combinatorial moves yields an automatic partition of the elements of the generated crystallization catalogue into equivalence classes, which turn out to be in one-to-one correspondence with the homeomorphism classes of the represented 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, 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 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 Computing JSJ decompositions of hyperbolic groups

2018 ◽  
Vol 11 (2) ◽  
pp. 527-558 ◽  
Author(s):  
Benjamin Barrett
Keyword(s):  
Hyperbolic Groups ◽  
Jsj Decompositions

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 QUASI-ISOMETRIES, BOUNDARIES AND JSJ-DECOMPOSITIONS OF RELATIVELY HYPERBOLIC GROUPS

2013 ◽  
Vol 05 (04) ◽  
pp. 451-475 ◽  
Author(s):  
BRADLEY W. GROFF
Keyword(s):  
Hyperbolic Groups ◽  
Isometry Groups ◽  
Geometric Structures ◽  
Relatively Hyperbolic Groups ◽  
Jsj Decomposition ◽  
Outer Automorphisms ◽  
Jsj Decompositions ◽  
Relatively Hyperbolic

We demonstrate the quasi-isometry invariance of two important geometric structures for relatively hyperbolic groups: the coned space and the cusped space. As applications, we produce a JSJ-decomposition for relatively hyperbolic groups which is invariant under quasi-isometries and outer automorphisms, as well as a related splitting of the quasi-isometry groups of relatively hyperbolic groups.

When does a right-angled Artin group split over ℤ?

2014 ◽  
Vol 24 (06) ◽  
pp. 815-825 ◽  
Author(s):  
Matt Clay
Keyword(s):  
Cyclic Subgroup ◽  
Artin Group ◽  
Artin Groups ◽  
Cyclic Subgroups ◽  
Right Angled Artin Groups ◽  
Jsj Decompositions

We show that a right-angled Artin group, defined by a graph Γ that has at least three vertices, does not split over an infinite cyclic subgroup if and only if Γ is biconnected. Further, we compute JSJ-decompositions of 1-ended right-angled Artin groups over infinite cyclic subgroups.

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