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The topological properties of the generalized Neuwirth groups, nk are discussed. For example, we demonstrate that the group, nk is the fundamental group of the Seifert fibered space Σnk. Moreover,… (More)

- Leonid A. Bokut, Andrei Vesnin
- J. Symb. Comput.
- 2006

Presenting 2-generator Artin groups A(m) and braid groups B"3 and B"4 as towers of HNN extensions of free groups, we obtain Grobner-Shirshov bases, normal forms and rewriting systems for these groups.

It is shown that if the defining word of a cyclically presented group is admissable then its natural HNN extension is the group of a high dimensional knot. As an example we define a family of… (More)

We introduce a family of closed 3-dimensional manifolds, which are a generalization of certain manifolds studied by M. Takahashi. The manifolds are represented by Dehn surgery with rational… (More)

We consider closed orientable 3-dimensional hyperbolic manifolds which are cyclic branched coverings of the 3-sphere, with branching set being a two-bridge knot (or link). We establish two-sided… (More)

We introduce two sequences of two-variable polynomials {LKn(t,l)} n=1∞ and {FKn(t,l)} n=1∞, expressed in terms of index value of a crossing and n-dwrithe value of a virtual knot K, where t and l ar...

Summary. We define a family of balanced presentations of groups and prove that they correspond to spines of some Seifert fibered 3-manifolds. These presentations of groups (and manifolds) generalize… (More)

Summary. - It has been proved by Accola that any 3-fold unbranched covering of a Riemann surface of genus two is hyperelliptic (a 2-fold branched covering of the 2-sphere) if the covering is… (More)

- Marco Reni, Andrei Vesnin
- 2001

Summary. - We consider hyperbolic 3-manifolds Mn(K), which are n-fold cyclic branched coverings of 2-bridge knots K. We show that for n ≥ 5 the orientation-preserving isometry group of Mn(K) either… (More)