Covering theory for complexes of groups

We develop an explicit covering theory for complexes of groups, parallel to that developed for graphs of groups by Bass. Given a covering of developable complexes of groups, we construct the induced monomorphism of fundamental groups and isometry of universal covers. We characterize faithful complexes of groups and prove a conjugacy theorem for groups acting freely on polyhedral complexes. We also define an equivalence relation on coverings of complexes of groups, which allows us to construct a bijection between such equivalence classes, and subgroups or overgroups of a fixed lattice $\Gamma$ in the automorphism group of a locally finite polyhedral complex $X$.Comment: 47 pages, 1 figure. Comprises Sections 1-4 of previous submission. New introduction. To appear in J. Pure Appl. Algebr

Divergence in right-angled Coxeter groups

Let W be a 2-dimensional right-angled Coxeter group. We characterise such W with linear and quadratic divergence, and construct right-angled Coxeter groups with divergence polynomial of arbitrary degree. Our proofs use the structure of walls in the Davis complex.Comment: This version incorporates the referee's comments. It contains the complete appendix (which will be abbreviated in the journal version). To appear in Transactions of the AM

Cocompact lattices in complete Kac-Moody groups with Weyl group right-angled or a free product of spherical special subgroups

Let G be a complete Kac-Moody group of rank n \geq 2 over the finite field of order q, with Weyl group W and building \Delta. We first show that if W is right-angled, then for all q \neq 1 mod 4 the group G admits a cocompact lattice \Gamma which acts transitively on the chambers of \Delta. We also obtain a cocompact lattice for q =1 mod 4 in the case that \Delta is Bourdon's building. As a corollary of our constructions, for certain right-angled W and certain q, the lattice \Gamma has a surface subgroup. We also show that if W is a free product of spherical special subgroups, then for all q, the group G admits a cocompact lattice \Gamma with \Gamma a finitely generated free group. Our proofs use generalisations of our results in rank 2 concerning the action of certain finite subgroups of G on \Delta, together with covering theory for complexes of groups.Comment: 19 pages. Version 2: we have generalised from Weyl group a free product of cyclic groups of order 2 to the two cases indicated by the new titl

Divergence in right-angled Coxeter groups

Let W be a 2-dimensional right-angled Coxeter group. We characterise such W with linear and quadratic divergence, and construct right-angled Coxeter groups with divergence polynomial of arbitrary degree. Our proofs use the structure of walls in the Davis complex

Partially Identified Prevalence Estimation under Misclassification using the Kappa Coefficient

We discuss a new strategy for prevalence estimation in the presence of misclassification. Our method is applicable when misclassification probabilities are unknown but independent replicate measurements are available. This yields the kappa coefficient, which indicates the agreement between the two measurements. From this information, a direct correction for misclassification is not feasible due to non-identifiability. However, it is possible to derive estimation intervals relying on the concept of partial identification. These intervals give interesting insights into possible bias due to misclassification. Furthermore, confidence intervals can be constructed. Our method is illustrated in several theoretical scenarios and in an example from oral health, where prevalence estimation of caries in children is the issue