2 citations · 4 across the 4 of their papers we have counts for
4 papers
On the homotopy type of the complement of an arrangement that is a 2-generic section of the parallel connection of an arrangement and a pencil of lines
Kristopher Williams
Let be a complexified-real arrangement of lines in Let be any line in . Then, form a new complexified-real arrangement $ \mathcal{…
A converse to a theorem of Oka and Sakamoto for complex line arrangements
Kristopher Williams
Let C_1 and C_2 be algebraic plane curves in the complex plane such that the curves intersect in d_1\cdot d_2 points where d_1,d_2 are the degrees of the curves respectively. Oka a…
The homology groups of the Milnor fiber associated to a central arrangement of hyperplanes in $\CC^3$
Kristopher Williams
We use covering space theory and the fundamental group of complements of complexified-real line arrangements to explore the associated Milnor fiber. This work yields a combinatoria…
Line arrangements and direct sums of free groups
Kristopher Williams
We show that if the fundamental groups of the complements of two line arrangements in the complex projective plane are isomorphic to the same direct sum of free groups, then the co…