5 papers · 1 filter
Representation asymptotics in the homology of pure graph braid groups
Louis Hainaut, Ben Knudsen, Nicholas Wawrykow
We give explicit formulas for the asymptotic Betti numbers, over an arbitrary field, of the ordered configuration spaces of a graph. In characteristic zero, we further give explici…
Lie algebras and the (co)homology of configuration spaces
Ben Knudsen
We survey decades of research identifying the (co)homology of configuration spaces with Lie algebra (co)homology. The different routes to this one proto-theorem offer genuinely dif…
On the analog category of finite groups
Ben Knudsen, Shmuel Weinberger
We show that the analog category of a finite group is essentially proportional to the size of its largest Sylow subgroup. We conclude that the universal upper bound given by the or…
Farber's conjecture and beyond
Ben Knudsen
We survey two decades of work on the (sequential) topological complexity of configuration spaces of graphs (ordered and unordered), aiming to give an account that is unifying, elem…
Analog category and complexity
Ben Knudsen, Shmuel Weinberger
We study probabilistic variants of the Lusternik--Schnirelmann category and topological complexity, which bound the classical invariants from below. We present a number of computat…