35 citations · 78 across the 14 of their papers we have counts for
14 papers
The Orlik--Solomon algebra of a locally geometric poset and cohomology of complex abelian arrangements
Christin Bibby, Peter Ramsey
We construct an Orlik--Solomon algebra for any locally geometric poset as a natural generalization of the one for geometric lattices. This algebra has several interesting features,…
On some structural properties of graphs with non-negative resistance curvature
Gyaneshwar Agrahari, Christin Bibby, Sean Boros +4
A graph is called resistance nonnegative (RN), respectively resistance positive (RP), if it admits positive edge weights such that all vertex resistance curvatures are nonnegative,…
Monodromy of supersolvable toric arrangements
Christin Bibby, Daniel C. Cohen, Emanuele Delucchi
We study topological aspects of supersolvable abelian arrangements, toric arrangements in particular. The complement of such an arrangement sits atop a tower of fiber bundles, and…
A Serre spectral sequence for the moduli space of tropical curves
Christin Bibby, Melody Chan, Nir Gadish +1
We construct, for all and , a spectral sequence of rational -representations which computes the -equivariant reduced rational cohomology of the tropica…
Matroid schemes and geometric posets
Christin Bibby
The intersection data of a hyperplane arrangement is described by a geometric lattice, or equivalently a simple matroid. There is a rich interplay between this combinatorial struct…
Supersolvable posets and fiber-type abelian arrangements
Christin Bibby, Emanuele Delucchi
We present a combinatorial analysis of fiber bundles of generalized configuration spaces on connected abelian Lie groups. These bundles are akin to those of Fadell-Neuwirth for con…
Homology representations of compactified configurations on graphs applied to
Christin Bibby, Melody Chan, Nir Gadish +1
We obtain new calculations of the top weight rational cohomology of the moduli spaces , equivalently the rational homology of the tropical moduli spaces $Δ_{2,n}…
A generating function approach to new representation stability phenomena in orbit configuration spaces
Christin Bibby, Nir Gadish
As countless examples show, it can be fruitful to study a sequence of complicated objects all at once via the formalism of generating functions. We apply this point of view to the…
A Leray model for the Orlik-Solomon algebra
Christin Bibby, Graham Denham, Eva Maria Feichtner
We construct a combinatorial generalization of the Leray models for hyperplane arrangement complements. Given a matroid and some combinatorial blowup data, we give a presentation f…
Minimal flag triangulations of lower-dimensional manifolds
Christin Bibby, Andrew Odesky, Mengmeng Wang +3
We prove the following results on flag triangulations of 2- and 3-manifolds. In dimension 2, we prove that the vertex-minimal flag triangulations of and $\mathbb{S…
Combinatorics of orbit configuration spaces
Christin Bibby, Nir Gadish
From a group action on a space, define a variant of the configuration space by insisting that no two points inhabit the same orbit. When the action is almost free, this "orbit conf…
Representation stability for the cohomology of arrangements associated to root systems
Christin Bibby
From a root system, one may consider the arrangement of reflecting hyperplanes, as well as its toric and elliptic analogues. The corresponding Weyl group acts on the complement of…
Quadratic-linear duality and rational homotopy theory of chordal arrangements
Christin Bibby, Justin Hilburn
To any graph and smooth algebraic curve one may associate a "hypercurve" arrangement and one can study the rational homotopy theory of the complement . In the rational case…
Cohomology of abelian arrangements
Christin Bibby
An abelian arrangement is a finite set of codimension one abelian subvarieties (possibly translated) in a complex abelian variety. In this paper, we study the cohomology of the com…