55 citations · 152 across the 12 of their papers we have counts for
12 papers
On Belk's classifying space for Thompson's group F
Lucas Sabalka, Matthew C. B. Zaremsky
The space of configurations of n ordered points in the plane serves as a classifying space for the pure braid group PB_n. Elements of Thompson's group F admit a model similar to br…
Submanifold Projection
Lucas Sabalka, Dmytro Savchuk
One of the most useful tools for studying the geometry of the mapping class group has been the subsurface projections of Masur and Minsky. Here we propose an analogue for the study…
On Restricting Subsets of Bases in Relatively Free Groups
Lucas Sabalka, Dmytro Savchuk
Let G be a finitely generated free, free abelian of arbitrary exponent, free nilpotent, or free solvable group, or a free group in the variety A_mA_n, and let A = {a_1,..., a_r} be…
On the geometry of a proposed curve complex analogue for
Lucas Sabalka, Dmytro Savchuk
The group $\Out$ of outer automorphisms of the free group has been an object of active study for many years, yet its geometry is not well understood. Recently, effort has been focu…
Face vectors of subdivided simplicial complexes
Emanuele Delucchi, Aaron Pixton, Lucas Sabalka
Brenti and Welker have shown that for any simplicial complex X, the face vectors of successive barycentric subdivisions of X have roots which converge to fixed values depending onl…
Multidimensional Online Robot Motion
Joshua Brown Kramer, Lucas Sabalka
We consider three related problems of robot movement in arbitrary dimensions: coverage, search, and navigation. For each problem, a spherical robot is asked to accomplish a motion-…
Projection-Forcing Multisets of Weight Changes
Josh Brown Kramer, Lucas Sabalka
Let be a finite field. A multiset of integers is projection-forcing if for every linear function whose multiset of weight changes is , is a coordina…
On rigidity and the isomorphism problem for tree braid groups
Lucas Sabalka
We solve the isomorphism problem for braid groups on trees with or 5 strands. We do so in three main steps, each of which is interesting in its own right. First, we establi…
On the cohomology rings of tree braid groups
Daniel Farley, Lucas Sabalka
Let be a finite connected graph. The (unlabelled) configuration space of points on is the space of -element subsets of . The -strand braid group of $Γ…
Embedding right-angled Artin groups into graph braid groups
Lucas Sabalka
We construct an embedding of any right-angled Artin group defined by a graph into a graph braid group. The number of strands required for the braid group is equal to the…
Discrete Morse theory and graph braid groups
Daniel Farley, Lucas Sabalka
If Gamma is any finite graph, then the unlabelled configuration space of n points on Gamma, denoted UC^n(Gamma), is the space of n-element subsets of Gamma. The braid group of Gamm…
Geodesics in the braid group on three strands
Lucas Sabalka
We study the geodesic growth series of the braid group on three strands, B_3 := <a,b|aba = bab>. We show that the set of geodesics of B_3 with respect to the generating set S := {a…