From the 1 of 5 linked papers with an AI index.
5 papers
Local-to-global fixed point properties for graphical C(4)-T(4) and C(6) small cancellation complexes
Karol Duda, Huaitao Gui
The paper proves that torsion subgroups of groups defined by certain graphical C(4)-T(4) and C(6) small cancellation presentations are finite, using local-to-global fixed point pro…
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…
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…
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…
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…