35 citations · 133 across the 18 of their papers we have counts for
20 papers
Motion planning invariants and families of subgroups
Ekansh Jauhari, Ben Knudsen
We introduce a notion of topological complexity of a group with respect to a family of subgroups, with the case of the trivial and diagonal families recovering the classical catego…
Corrigendum to "Asymptotic homology of graph braid groups"
Byung Hee An, Gabriel C. Drummond-Cole, Ben Knudsen
We correct an error in the paper referred to in the title. Part of the argument is organized as a general method for establishing when (derived) functors factor through a fixed Ser…
Robertson's conjecture and universal finite generation in the homology of graph braid groups
Ben Knudsen, Eric Ramos
We formulate a categorification of Robertson's conjecture analogous to the categorical graph minor conjecture of Miyata--Proudfood--Ramos. We show that these conjectures imply the…
On the stabilization of the topological complexity of graph braid groups
Ben Knudsen
We establish a strong, geometric lower bound on the (sequential) topological complexity of the unordered configuration spaces of a general graph. As an application, we show that, f…
The topological complexity of pure graph braid groups is stably maximal
Ben Knudsen
We prove Farber's conjecture on the stable topological complexity of configuration spaces of graphs. The conjecture follows from a general lower bound derived from recent insights…
Projection spaces and twisted Lie algebras
Ben Knudsen
A projection space is a collection of spaces interrelated by the combinatorics of projection onto tensor factors in a symmetric monoidal background category. Examples include class…
Extremal stability for configuration spaces
Ben Knudsen, Jeremy Miller, Philip Tosteson
We study stability patterns in the high dimensional rational homology of unordered configuration spaces of manifolds. Our results follow from a general approach to stability phenom…
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…
On the second homology of planar graph braid groups
Byung Hee An, Ben Knudsen
We show that the second homology of the configuration spaces of a planar graph is generated under the operations of embedding, disjoint union, and edge stabilization by three atomi…
Embedding calculus and smooth structures
Ben Knudsen, Alexander Kupers
We study the dependence of the embedding calculus Taylor tower on the smooth structures of the source and target. We prove that embedding calculus does not distinguish exotic smoot…
Asymptotic homology of graph braid groups
Byung Hee An, Gabriel C. Drummond-Cole, Ben Knudsen
We give explicit formulas for the asymptotic Betti numbers of the unordered configuration spaces of an arbitrary finite graph over an arbitrary field.
The Lubin-Tate Theory of Configuration Spaces: I
Lukas Brantner, Jeremy Hahn, Ben Knudsen
We construct a spectral sequence converging to the Morava -theory of unordered configuration spaces and identify its E-page as the homology of a Chevalley-Eilenberg-like com…
A Kuenneth theorem for configuration spaces
Kathryn Hess, Ben Knudsen
We construct a spectral sequence converging to the homology of the ordered configuration spaces of a product of parallelizable manifolds. To identify the second page of this spectr…
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…
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…
Configuration spaces of products
William Dwyer, Kathryn Hess, Ben Knudsen
We show that the configuration spaces of a product of parallelizable manifolds may be recovered from those of the factors as the Boardman-Vogt tensor product of right modules over…
Subdivisional spaces and graph braid groups
Byung Hee An, Gabriel C. Drummond-Cole, Ben Knudsen
We study the problem of computing the homology of the configuration spaces of a finite cell complex . We proceed by viewing , together with its subdivisions, as a subdivision…
Betti numbers of configuration spaces of surfaces
Gabriel C. Drummond-Cole, Ben Knudsen
We give explicit formulas for the Betti numbers, both stable and unstable, of the unordered configuration spaces of an arbitrary surface of finite type.
Higher enveloping algebras
Ben Knudsen
We provide spectral Lie algebras with enveloping algebras over the operad of little -framed -dimensional disks for any choice of dimension and structure group , and we…
Betti numbers and stability for configuration spaces via factorization homology
Ben Knudsen
Using factorization homology, we realize the rational homology of the unordered configuration spaces of an arbitrary manifold , possibly with boundary, as the homology of a Lie…