scholarly journals THE FIGURE EIGHT KNOT GROUP IS CONJUGACY SEPARABLE

2009 ◽  
Vol 08 (04) ◽  
pp. 539-556 ◽  
Author(s):  
S. C. CHAGAS ◽  
P. A. ZALESSKII
Keyword(s):  
Figure Eight Knot ◽  
Free Subgroups ◽  
Conjugacy Separable ◽  
Torsion Free

We prove that torsion free subgroups of GL2(ℂ) (abstractly) commensurable with the Euclidean Bianchi groups are conjugacy separable. As a consequence we deduce the result stated in the tittle.

scholarly journals A family of conformally asymmetric Riemann surfaces

1997 ◽  
Vol 39 (2) ◽  
pp. 221-225 ◽  
Author(s):  
Brent Everitt
Keyword(s):  
Automorphism Group ◽  
Riemann Surfaces ◽  
Coset Diagrams ◽  
Free Subgroups ◽  
Torsion Free

AbstractWe give explicit examples of asymmetric Riemann surfaces (that is, Riemann surfaces with trivial conformal automorphism group) for all genera g ≥ 3. The technique uses Schreier coset diagrams to construct torsion-free subgroups in groups of signature (0; 2,3,r) for certain values of r.

ON A TORSION-FREE WEAKLY BRANCH GROUP DEFINED BY A THREE STATE AUTOMATON

2002 ◽  
Vol 12 (01n02) ◽  
pp. 223-246 ◽  
Author(s):  
ROSTISLAV I. GRIGORCHUK ◽  
ANDRZEJ ŻUK
Keyword(s):  
Forthcoming Paper ◽  
Galois Groups ◽  
Branch Group ◽  
Free Subgroups ◽  
Torsion Free

We study a torsion free weakly branch group G without free subgroups defined by a three state automaton which appears in different problems related to amenability, Galois groups and monodromy. Here and in the forthcoming paper [20] we establish several important properties of G related to fractalness, branchness, just infinitness, growth, amenability and presentations.

scholarly journals Non-Left-Orderable 3-Manifold Groups

2005 ◽  
Vol 48 (1) ◽  
pp. 32-40 ◽  
Author(s):  
Mieczysław K. Dąbkowski ◽  
Józef H. Przytycki ◽  
Amir A. Togha
Keyword(s):  
Special Interest ◽  
Branched Covers ◽  
Branched Coverings ◽  
Figure Eight Knot ◽  
Torsion Free

AbstractWe show that several torsion free 3-manifold groups are not left-orderable. Our examples are groups of cyclic branched coverings of S3 branched along links. The figure eight knot provides simple nontrivial examples. The groups arising in these examples are known as Fibonacci groups which we show not to be left-orderable. Many other examples of non-orderable groups are obtained by taking 3-fold branched covers of S3 branched along various hyperbolic 2-bridge knots. The manifold obtained in such a way from the 52 knot is of special interest as it is conjectured to be the hyperbolic 3-manifold with the smallest volume.

scholarly journals Torsion free subgroups of fuchsian groups and tessellations of surfaces

1982 ◽  
Vol 69 (3) ◽  
pp. 331-346 ◽  
Author(s):  
Allan L. Edmonds ◽  
John H. Ewing ◽  
Ravi S. Kulkarni
Keyword(s):  
Fuchsian Groups ◽  
Free Subgroups ◽  
Torsion Free

scholarly journals Classifying torsion-free subgroups of the Picard group

1984 ◽  
Vol 282 (1) ◽  
pp. 205-205 ◽  
Author(s):  
Andrew M. Brunner ◽  
Michael L. Frame ◽  
Youn W. Lee ◽  
Norbert J. Wielenberg
Keyword(s):  
Picard Group ◽  
Free Subgroups ◽  
Torsion Free
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