Combinatorics Seminar
by Colin Crowley (University of Oregon)
We consider the space of configurations of n points in the three-sphere S^3, some pairs of which are allowed to coincide and some pairs of which are not, up to the free and transitive action of SU(2) on S^3. We prove that the cohomology ring with rational coefficients is isomorphic to an internal zonotopal algebra, which is a combinatorially defined ring appearing independently in the work of Holtz and Ron and of Ardila and Postnikov. We use zonotopal algebras to prove a conjecture of Moseley, Proudfoot, and Young relating the cohomology of these configuration spaces and the Orlik-Terao algebra. Based on joint work with Galen Dorpalen-Barry, André Henriques, and Nicholas Proudfoot.
https://arxiv.org/abs/2502.12768
