Largeness and Sq-Universality of cyclically Presented Groups

Tadpole Labelled Oriented Graph Groups and Cyclically Presented Groups

We study a class of Labelled Oriented Graph (LOG) group where the underlying graph is a tadpole graph. We show that such a group is the natural HNN extension of a cyclically presented group and investigate the relationship between the LOG group and the cyclically presented group. We relate the second homotopy groups of their presentations and show that hyperbolicity of the cyclically presented ...

Udc 512.543.7+512.543.16 the Sq-universality of One-relator Relative Presentations

Adding two generators and one arbitrary relator to a nontrivial torsion-free group, we always obtain an SQ-universal group. In the course of the proof of this theorem, we obtain some other results of independent interest. For instance, adding one generator and one relator in which the exponent sum of the additional generator is one to a free product of two nontrivial torsion-free groups, we als...

On the Structure of Some Deficiency Zero Groups

Eigenfunction Statistics of Complex Systems: A Single Parametric Formulation

We derive a common mathematical formulation for the eigenvector statistics of Hermitian operators, represented by a multi-parametric probability density. The system-information in the formulation enters through a single function of all system parameter, thus indicating a single parameter scaling of the statistics. This in turn reveals a deep rooted universality hidden underneath the world of co...

Cyclically presented groups in which the relators involve at most three generators

Cyclically presented groups Gn(w) in which w involves at most three generators are studied. We classify when such groups have infinite abelianizations and apply this result to the groups Gn(x1x1+kx 1+`). As a further corollary we give sufficient conditions for the natural HNN extension of Gn(w) to be a high-dimensional knot group. By continuing Cavicchioli, Repovš, and Spaggiari’s investigation...