11 citations · 14 across the 6 of their papers we have counts for
7 papers
Filtrations of Tope Spaces of Oriented Matroids
Kris Shaw, Chi Ho Yuen
We compare three filtrations of the tope space of an oriented matroid. The first is the dual Varchenko-Gelfand degree filtration, the second filtration is from Kalinin's spectral s…
The omega invariant of a matroid
Alex Fink, Kris Shaw, David E Speyer
The third author introduced the -polynomial of a matroid, a covaluative matroid statistic which is unchanged under series and parallel extension. The -polynomial of…
Real phase structures on tropical manifolds and patchworks in higher codimension
Johannes Rau, Arthur Renaudineau, Kris Shaw
This paper generalises the homeomorphism theorem behind Viro's combinatorial patchworking of hypersurfaces in toric varieties to arbitrary codimension using tropical geometry. We f…
Chern Classes of Tropical Manifolds
Lucía López de Medrano, Felipe Rincón, Kris Shaw
We extend the definitions of Chern-Schwartz-MacPherson (CSM) cycles of matroids to tropical manifolds. To do this, we provide an alternate description of CSM cycles of matroids whi…
Tropical compactification via Ganter's algorithm
Lars Kastner, Kristin Shaw, Anna-Lena Winz
We describe a canonical compactification of a polyhedral complex in Euclidean space. When the recession cones of the polyhedral complex form a fan, the compactified polyhedral comp…
Lefschetz section theorems for tropical hypersurfaces
Charles Arnal, Arthur Renaudineau, Kristin Shaw
We establish variants of the Lefschetz hyperplane section theorem for the integral tropical homology groups of tropical hypersurfaces of toric varieties. It follows from these theo…
Bounding the Betti numbers of real hypersurfaces near the tropical limit
Arthur Renaudineau, Kristin Shaw
We prove a bound conjectured by Itenberg on the Betti numbers of real algebraic hypersurfaces near non-singular tropical limits. These bounds are given in terms of the Hodge number…