3 papers
math.AT2020
Farber's conjecture for planar graphs
Ben Knudsen
We prove that the ordered configuration spaces of planar graphs have the highest possible topological complexity generically, as predicted by a conjecture of Farber. Our argument e…
math.GT2018
Edge stabilization in the homology of graph braid groups
Byung Hee An, Gabriel C. Drummond-Cole, Ben Knudsen
We introduce a novel type of stabilization map on the configuration spaces of a graph, which increases the number of particles occupying an edge. There is an induced action on homo…
math.AT2018
Configuration spaces in algebraic topology
Ben Knudsen
These expository notes are dedicated to the study of the topology of configuration spaces of manifolds. We give detailed computations of many invariants, including the fundamental…