25 citations · 146 across the 36 of their papers we have counts for
43 papers
Hierarchical hyperbolicity, ball quotients, and the moduli space of smooth cubic surfaces
Daniel Allcock, Alex Wright
We prove that the orbifold fundamental group of the moduli space of smooth complex cubic surfaces is a hierarchically hyperbolic group. This places it within a powerful geometric f…
Arithmetic Polyhedra
Daniel Allcock, Pat Devlin, Anna Felikson +2
The Koebe-Andreev-Thurston theorem assigns a 3-dimensional hyperbolic reflection group to each combinatorial polyhedron. A natural question is: which of them are arithmetic? In 201…
The Deligne-Mostow 9-ball, and the monster
Daniel Allcock, Tathagata Basak
The "monstrous proposal" of the first author is that the quotient of a certain 13-dimensional complex hyperbolic braid group, by the relations that its natural generators have orde…
An Alternative to Vinberg's Algorithm
Daniel Allcock
Vinberg's algorithm is the main method for finding fundamental domains for reflection groups acting on hyperbolic space. Experience shows that it can be slow. We explain why this s…
Most big mapping class groups fail the Tits Alternative
Daniel Allcock
Let be a surface, possibly with boundary. Suppose it has infinite genus or infinitely many punctures, or a closed subset which is a disk with a Cantor set removed from its inte…
Variations on Glauberman's ZJ Theorem
Daniel Allcock
We give a new proof of Glauberman's ZJ Theorem, in a form that clarifies the choices involved and offers more choices than classical treatments. In particular, we introduce two new…