25 citations · 146 across the 36 of their papers we have counts for
19 papers · 1 filter
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…
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…
Presentation of hyperbolic Kac-Moody groups over rings
Daniel Allcock, Lisa Carbone
Tits has defined Kac-Moody and Steinberg groups over commutative rings, providing infinite dimensional analogues of the Chevalley-Demazure group schemes. Here we establish simple e…
Prenilpotent pairs in the E10 root system
Daniel Allcock
Tits has defined Kac-Moody groups for all root systems, over all commutative rings with unit. A central concept is the idea of a prenilpotent pair of (real) roots. In particular, w…