Hyperfield Grassmannians
Copyright policy )Hyperfield Grassmannians
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
Oriented matroids in discrete geometry, Grassmannian, Geometric Topology (math.GT), Combinatorial aspects of matroids and geometric lattices, realization space, hyperfield, oriented matroid, Mathematics - Algebraic Geometry, Mathematics - Geometric Topology, Tropical geometry, tropical hyperfield, FOS: Mathematics, matroid, Mathematics - Combinatorics, Algebraic Topology (math.AT), 05B35 (primary), 52C40, 52B40, 57R20, 54H13, 12J99 (secondary), Mathematics - Algebraic Topology, Combinatorics (math.CO), Algebraic Geometry (math.AG)
Oriented matroids in discrete geometry, Grassmannian, Geometric Topology (math.GT), Combinatorial aspects of matroids and geometric lattices, realization space, hyperfield, oriented matroid, Mathematics - Algebraic Geometry, Mathematics - Geometric Topology, Tropical geometry, tropical hyperfield, FOS: Mathematics, matroid, Mathematics - Combinatorics, Algebraic Topology (math.AT), 05B35 (primary), 52C40, 52B40, 57R20, 54H13, 12J99 (secondary), Mathematics - Algebraic Topology, Combinatorics (math.CO), Algebraic Geometry (math.AG)
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