arXiv subjects
Publications and source records attributed to Daniel Wise.
Two seemingly different properties of 2-complexes were developed concurrently as criteria for the nonpositive immersion property: 'good stackings' and 'bislim structures'. We establish an equivalence between these properties by introducing a third property 'invariant staggerings' mediating between them.
We study the problem of extending partial isomorphisms for hypertournaments, which are relational structures generalizing tournaments. This is a generalized version of an old question of Herwig and Lascar. We show that the generalized problem has a negative answer, and we provide a positive answer in a special case. As a corollary, we show that the extension property holds for tournaments in case the partial isomorphisms have pairwise disjoint ranges and pairwise disjoint domains.
In this article we prove new results about the existence of 2-cells in disc diagrams which are extreme in the sense that they are attached to the rest of the diagram along a small connected portion of their boundary cycle. In particular, we establish conditions on a 2-complex X which imply that all minimal area disc diagrams over X with reduced boundary cycles have extreme 2-cells in this sense. The existence of extreme 2-cells in disc diagrams over these complexes leads to new results on coherence using the perimeter-reduction techniques we developed in an earlier article. Recall that a group is called coherent if all of its finitely generated subgroups are finitely presented. We illustrate this approach by showing that several classes of one-relator groups, small cancellation groups and groups with staggered presentations are collections of coherent groups.