arXiv subjects

Daniel Danielski

Publications and source records attributed to Daniel Danielski.

5 recordsLinked to original sources

arXiv2025

On boundaries of bicombable spaces

We initiate systematic study of EZ-structures (and associated boundaries) of groups acting on spaces that admit consistent and conical (equivalently, consistent and convex) geodesic bicombings. Such spaces recently drew a lot of attention due to the fact that many classical groups act `nicely' on them. We rigorously construct EZ-structures, discuss their uniqueness (up to homeomorphism), provide examples, and prove some boundary-related features analogous to the ones exhibited by CAT(0) spaces and groups, which form a subclass of the discussed class of spaces and groups.

math.GR↗

arXiv2022

Right-angled Coxeter groups with Menger curve boundary

We find a sufficient condition for a nerve of a hyperbolic right-angled Coxeter group, under which the boundary of the group is homeomorphic to the Menger curve. We show that this condition is satisfied by many triangulations of surfaces with boundary and other 2-complexes, as well as by some triangulations of disks $D^n$ for arbitrary $n\geq3$.

math.GT↗

arXiv2021

Complete characterizations of hyperbolic Coxeter groups with Sierpi\'nski curve boundary and with Menger curve boundary

We give complete characterizations (in terms of nerves) of those word hyperbolic Coxeter groups whose Gromov boundary is homeomorphic to the Sierpi\'nski curve and to the Menger curve, respectively. The justification is mostly an appropriate combination of various results from the literature.

math.GT↗

arXiv2019

Finite Satisfiability of Unary Negation Fragment with Transitivity

We show that the finite satisfiability problem for the unary negation fragment with arbitrary number of transitive relations is decidable and 2-ExpTime-complete. Our result actually holds for a more general setting in which one can require that some binary symbols are interpreted as arbitrary transitive relations, some as partial orders and some as equivalences. We also consider finite satisfiability of various extensions of our primary logic, in particular capturing the concepts of nominals and role hierarchies known from description logic. As the unary negation fragment can express unions of conjunctive queries our results have interesting implications for the problem of finite query answering, both in the classical scenario and in the description logics setting.

cs.LO↗

arXiv2018

Unary negation fragment with equivalence relations has the finite model property

We consider an extension of the unary negation fragment of first-order logic in which arbitrarily many binary symbols may be required to be interpreted as equivalence relations. We show that this extension has the finite model property. More specifically, we show that every satisfiable formula has a model of at most doubly exponential size. We argue that the satisfiability (= finite satisfiability) problem for this logic is TwoExpTime-complete. We also transfer our results to a restricted variant of the guarded negation fragment with equivalence relations.

cs.LO↗