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 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 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 L-space intervals for graph manifolds and cables

2017 ◽  
Vol 153 (5) ◽  
pp. 1008-1049 ◽  
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.

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

2014 ◽  
Vol 35 (6) ◽  
pp. 1681-1722 ◽  
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.

scholarly journals Higher even dimensional Reidemeister torsion for torus knot exteriors

2013 ◽  
Vol 155 (2) ◽  
pp. 297-305 ◽  
Author(s):  
YOSHIKAZU YAMAGUCHI
Keyword(s):  
Reidemeister Torsion ◽  
Torus Knot ◽  
Higher Dimensional ◽  
Hyperbolic Volumes

AbstractWe study the asymptotics of the higher dimensional Reidemeister torsion for torus knot exteriors, which is related to the results by W. Müller and P. Menal–Ferrer and J. Porti on the asymptotics of the Reidemeister torsion and the hyperbolic volumes for hyperbolic 3-manifolds. We show that the sequence of 1/(2N)2) log | Tor(EK; ρ2N)| converges to zero when N goes to infinity where TorEK; ρ2N is the higher dimensional Reidemeister torsion of a torus knot exterior and an acyclic SL2N(ℂ)-representation of the torus knot group. We also give a classification for SL2(ℂ)-representations of torus knot groups, which induce acyclic SL2N(ℂ)-representations.

scholarly journals Magnetic String with a NonlinearU(1)Source

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
S. H. Hendi
Keyword(s):  
Asymptotic Behavior ◽  
Magnetic Fields ◽  
Electromagnetic Fields ◽  
Einstein Gravity ◽  
Rotation Parameter ◽  
Conserved Quantities ◽  
Curvature Singularity ◽  
Conic Singularity ◽  
Higher Dimensional ◽  
Rotation Parameters

Considering the Einstein gravity in the presence of Born-Infeld type electromagnetic fields, we introduce a class of 4-dimensional static horizonless solutions which produce longitudinal magnetic fields. Although these solutions do not have any curvature singularity and horizon, there exists a conic singularity. We investigate the effects of nonlinear electromagnetic fields on the properties of the solutions and find that the asymptotic behavior of the solutions is adS. Next, we generalize the static metric to the case of rotating solutions and find that the value of the electric charge depends on the rotation parameter. Furthermore, conserved quantities will be calculated through the use of the counterterm method. Finally, we extend four-dimensional magnetic solutions to higher dimensional solutions. We present higher dimensional rotating magnetic branes with maximum rotation parameters and obtain their conserved quantities.

FOUR- AND HIGHER-DIMENSIONAL MODELS WITH DILATON–ELECTROMAGNETIC FIELDS

2001 ◽  
Vol 10 (04) ◽  
pp. 523-528 ◽  
Author(s):  
NARAYAN CHANDRA CHAKRABORTY ◽  
SUBENOY CHAKRABORTY
Keyword(s):  
Asymptotic Behavior ◽  
Electromagnetic Fields ◽  
Dilaton Field ◽  
Field Equations ◽  
General Solutions ◽  
Higher Dimensional ◽  
Bianchi Iii ◽  
Dimensional Models ◽  
Frw Models

The Einstein–Maxwell dilaton field equations are constructed for four-dimensional Bianchi III and five-dimensional FRW models. The general solutions have been obtained and their asymptotic behavior have been studied.

Sign in / Sign up

Export Citation Format

Share Document