Mathematics

Recent Papers:

• William A. Bogley, Martin Edjvet, and Gerald Williams, Aspherical relative presentations all over again, to appear in Groups St. Andrews 2017 (31 pp). arXiv:1809.03460.
• Willam A. Bogley and Forrest W. Parker, Cyclically presented groups with length four positive relators, J. Group Theory 21 (2018), 911-948, published online 6/15/2018. arXiv:1611.05496
• W. A. Bogley and Gerald Williams, Coherence, subgroup separability, and metacyclic structures for a class of cyclically presented groups, J. Algebra 480 (2017) 266–297. arXiv:1606.00216
• W. A. Bogley and Gerald Williams, Efficient finite groups arising in the study of relative asphericity, Math. Z. (2016) 284:507–535. PDF arXiv:1607.01951
• W. A. Bogley, On shift dynamics for cyclically presented groups, J. Algebra 418 (2014), 154-173. PDF arXiv:1312.5382

Areas of interest and publication:

1. Structure and shift dynamics for cyclically (and symmetrically) presented groups
2. Asphericity of cell complexes and cohomology of groups
3. Relative homotopy groups and equations over groups
4. Actions on cell complexes and finiteness properties of groups
5. Combinatorial geometry and algorithmic/decidability properties of groups
6. Wild metric cell complexes and omega-group structures, in which certain infinite products can be formed subject to suitable generalizations of the associativity axiom.