Matches in SemOpenAlex for { <https://semopenalex.org/work/W2977291569> ?p ?o ?g. }
- W2977291569 abstract "To a graph, Hausel and Proudfoot associate two complex manifolds, $mathfrak{B}$ and $mathfrak{D}$, which behave, respectively, like moduli of local systems on a Riemann surface and moduli of Higgs bundles. For instance, $mathfrak{B}$ is a moduli space of microlocal sheaves, which generalize local systems, and $mathfrak{D}$ carries the structure of a complex integrable system. We show the Euler characteristics of these varieties count spanning subtrees of the graph, and the point-count over a finite field for $mathfrak{B}$ is a generating polynomial for spanning subgraphs. This polynomial satisfies a deletion-contraction relation, which we lift to a deletion-contraction exact triangle for the cohomology of $mathfrak{B}$. There is a corresponding triangle for $mathfrak{D}$. Finally, we prove that $mathfrak{B}$ and $mathfrak{D}$ are diffeomorphic, the diffeomorphism carries the weight filtration on the cohomology of $mathfrak{B}$ to the perverse Leray filtration on the cohomology of $mathfrak{D}$, and all these structures are compatible with the deletion-contraction triangles." @default.
- W2977291569 created "2019-10-10" @default.
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- W2977291569 date "2023-08-03" @default.
- W2977291569 modified "2023-09-23" @default.
- W2977291569 title "Deletion-contraction triangles for Hausel–Proudfoot varieties" @default.
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- W2977291569 doi "https://doi.org/10.4171/jems/1369" @default.
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