25 citations · 146 across the 36 of their papers we have counts for
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Braid pictures for Artin groups
Daniel Allcock
We define the braid groups of a two-dimensional orbifold and introduce conventions for drawing braid pictures. We use these to realize the Artin groups associated to the spherical…
New complex- and quaternion-hyperbolic reflection groups
Daniel Allcock
We consider the automorphism groups of various Lorentzian lattices over the Eisenstein, Gaussian, and Hurwitz integers, and in some of them we find reflection groups of finite inde…
The Period Lattice for Enriques Surfaces
Daniel Allcock
We simplify the usual statement of the Torelli theorem for complex Enriques surfaces, by means of a lattice-theoretic trick. This allows easy proofs of several known results, which…
Metric curvature of infinite branched covers
Daniel Allcock
We study branched covering spaces in several contexts, proving that under suitable circumstances the cover satisfies the same upper curvature bounds as the base space. The first co…