8 papers
Local-to-global fixed point properties for graphical C(4)-T(4) and C(6) small cancellation complexes
Karol Duda, Huaitao Gui
Graphical small cancellation extends the classical small cancellation theory and provides a powerful method for constructing groups with prescribed subgraphs in their Cayley graphs…
The small cancellation flat torus theorem
Karol Duda
We establish Flat Torus Theorem type results for groups acting on small cancellation complexes satisfying C(6), C(4)-T(4) and C(3)-T(6) conditions. For C(3)-T(6) complexes the resu…
Hall's Harem Theorem with controlled sizes of cycles
Karol Duda
We prove a new version of Hall's Harem Theorem, where the final matching is realized by a unary function with additional conditions on behavior of cycles. The present paper can be…
Computable Folner sequences of amenable groups
Karol Duda, Aleksander Ivanov
The paper considers computable Folner sequences in computably enumerable amenable groups. We extend some basic results of M. Cavaleri on existence of such sequences to the case of…
Computable paradoxical decompositions
Karol Duda, Aleksander Ivanov
We prove a computable version of Hall's Harem Theorem and apply it to computable versions of Tarski's alternative theorem.
Torsion subgroups of small cancellation groups
Karol Duda
We prove that torsion subgroups of groups defined by C(6), C(4)-T(4) or C(3)-T(6) small cancellation presentations are finite cyclic groups. This follows from a more general result…
A computable version of Hall's Harem Theorem and Geometric von Neumann Conjecture
Karol Duda
We prove a computable version of the Hall Harem Theorem where the matching realizes a unary function with controlled sizes of cycles. We apply it to non-amenable computable coarse…
Amenability and computability
Karol Duda
In this paper we extend the approach of M. Cavaleri to effective amenability to the class of computably enumerable groups, i.e. in particular we do not assume that groups are finit…