Hyperfield Grassmannians
arXiv:1710.00016 · doi:10.1016/j.aim.2018.10.021
Abstract
In a recent paper Baker and Bowler introduced matroids over hyperfields, offering a common generalization of matroids, oriented matroids, and linear subspaces of based vector spaces. This paper introduces the notion of a topological hyperfield and explores the generalization of Grassmannians and realization spaces to this context, particularly in relating the (hyper)fields R and C to hyperfields arising in matroid theory and in tropical geometry.
31 pages. Final version