9 citations · 14 across the 5 of their papers we have counts for
6 papers
Pure braid groups are not residually free
Daniel C. Cohen, Michael Falk, Richard Randell
We show that the Artin pure braid group on at least four strands is not residually free. Our results also show that the pure braid group on at least three strands has corank two.
Discriminantal bundles, arrangement groups, and subdirect products of free groups
Daniel C. Cohen, Michael J. Falk, Richard C. Randell
We construct bundles $E_k(\A,\F) \to M$ over the complement of a complex hyperplane arrangement \A, depending on an integer and a set $\F=\{f_1, \ldots, f_μ\}$ of co…
Homotopy groups and twisted homology of arrangements
Richard Randell
Recent work of M. Yoshinaga shows that in some instances certain higher homotopy groups of arrangements map onto non-resonant homology. This is in contrast to the usual Hurewicz ma…
Mobius transformations of polygons and partitions of 3-space
Richard Randell, Jonathan Simon, Joshua Tokle
The image of a polygonal knot K under a spherical inversion of R^3 (union infinity) is a simple closed curve made of arcs of circles, having the same knot type as the mirror image…
Morse theory, Milnor fibers and minimality of hyperplane arrangements
Richard Randell
Through the study of Morse theory on the associated Milnor fiber, we show that complex hyperplane arrangement complements are minimal. That is, the complement of a complex hyperpla…
On the homotopy theory of arrangements, II
Michael Falk, Richard Randell
In "On the homotopy theory of arrangements," published in 1986, the authors gave a comprehensive survey of the subject. This article updates and continues the earlier article, noti…