scholarly journals On the conjugacy problem for knot groups

1973 ◽  
pp. 18-18
Author(s):  
K. I. Appel
Keyword(s):  
Conjugacy Problem

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.

On the conjugacy problem for carter subgroups

1998 ◽  
Vol 26 (2) ◽  
pp. 395-399 ◽  
Author(s):  
F.Dalla Volta ◽  
A. Lucchini ◽  
M.C. Tamburini
Keyword(s):  
Conjugacy Problem

scholarly journals Time complexity of the conjugacy problem in relatively hyperbolic groups

2015 ◽  
Vol 25 (05) ◽  
pp. 689-723 ◽  
Author(s):  
Inna Bumagin
Keyword(s):  
Polynomial Time ◽  
Positive Curvature ◽  
Nauk Sssr ◽  
Hyperbolic Group ◽  
Conjugacy Problem ◽  
Hyperbolic Groups ◽  
Search Problem ◽  
Relatively Hyperbolic Groups ◽  
Relatively Hyperbolic Group ◽  
Relatively Hyperbolic

If u and v are two conjugate elements of a hyperbolic group then the length of a shortest conjugating element for u and v can be bounded by a linear function of the sum of their lengths, as was proved by Lysenok in [Some algorithmic properties of hyperbolic groups, Izv. Akad. Nauk SSSR Ser. Mat. 53(4) (1989) 814–832, 912]. Bridson and Haefliger showed in [Metrics Spaces of Non-Positive Curvature (Springer-Verlag, Berlin, 1999)] that in a hyperbolic group the conjugacy problem can be solved in polynomial time. We extend these results to relatively hyperbolic groups. In particular, we show that both the conjugacy problem and the conjugacy search problem can be solved in polynomial time in a relatively hyperbolic group, whenever the corresponding problem can be solved in polynomial time in each parabolic subgroup. We also prove that if u and v are two conjugate hyperbolic elements of a relatively hyperbolic group then the length of a shortest conjugating element for u and v is linear in terms of their lengths.

The Boone-Higman theorem and the conjugacy problem

1977 ◽  
Vol 49 (1) ◽  
pp. 212-221 ◽  
Author(s):  
George S Sacerdote
Keyword(s):  
Conjugacy Problem

scholarly journals The conjugacy problem for Coxeter groups

2009 ◽  
pp. 71-171 ◽  
Author(s):  
Daan Krammer
Keyword(s):  
Coxeter Groups ◽  
Conjugacy Problem

scholarly journals Hartman’s theorem for hyperbolic sets

1977 ◽  
Vol 67 ◽  
pp. 41-52 ◽  
Author(s):  
Masahiro Kurata
Keyword(s):  
Fixed Point ◽  
Finite Type ◽  
Conjugacy Problem ◽  
Topological Conjugacy ◽  
Shift Of Finite Type ◽  
Linear Map ◽  
Hyperbolic Set ◽  
Slight Extension ◽  
Hyperbolic Fixed Point ◽  
Hyperbolic Sets

Hartman proved that a diffeomorphism is topologically conjugate to a linear map on a neighbourhood of a hyperbolic fixed point ([3]). In this paper we study the topological conjugacy problem of a diffeomorphism on a neighbourhood of a hyperbolic set, and prove that for any hyperbolic set there is an arbitrarily slight extension to which a sub-shift of finite type is semi-conjugate.

scholarly journals Orbit decidability and the conjugacy problem for some extensions of groups

2009 ◽  
Vol 362 (04) ◽  
pp. 2003-2036 ◽  
Author(s):  
O. Bogopolski ◽  
A. Martino ◽  
E. Ventura
Keyword(s):  
Conjugacy Problem

scholarly journals Holonomic and Legendrian parametrizations of knots

2000 ◽  
Vol 09 (03) ◽  
pp. 293-309 ◽  
Author(s):  
Joan S. Birman ◽  
Nancy C. Wrinkle
Keyword(s):  
Conjugacy Problem ◽  
Braid Groups ◽  
Algebraic Solution ◽  
Legendrian Knots

Holonomic parametrizations of knots were introduced in 1997 by Vassiliev, who proved that every knot type can be given a holonomic parametrization. Our main result is that any two holonomic knots which represent the same knot type are isotopic in the space of holonomic knots. A second result emerges through the techniques used to prove the main result: strong and unexpected connections between the topology of knots and the algebraic solution to the conjugacy problem in the braid groups, via the work of Garside. We also discuss related parametrizations of Legendrian knots, and uncover connections between the concepts of holonomic and Legendrian parametrizations of knots.

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