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math.CO2025
On graphs, homology bases, and triangulated homology spheres
Karim Adiprasito, Marc Lackenby, Juan Souto +1
We describe a construction that takes as input a graph and a basis for its first homology, and returns a triangulation of a 3-dimensional homology sphere. This makes precise an ide…
math.CO2025
-anisotropy on the moment curve for homology manifolds and cycles
Karim Adiprasito, Kaiying Hou, Daishi Kiyohara +2
We prove that the Gorensteinification of the face ring of a cycle is totally -anisotropic in characteristic . In other words, given an appropriate Artinian reduction, it cont…
math.CO2024
All triangulations have a common stellar subdivision
Karim Adiprasito, Igor Pak
We address two longstanding open problems, one originating in PL topology, another in birational geometry. First, we prove the weighted version of Oda's \emph{strong factorization…