We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
Deletion-contraction triangles for Hausel--Proudfoot varieties.
- Authors
Dancso, Zsuzsanna; McBreen, Michael; Shende, Vivek
- Abstract
To a graph, Hausel and Proudfoot associate two complex manifolds, B and D, which behave, respectively, like moduli of local systems on a Riemann surface and moduli of Higgs bundles. For instance, B is a moduli space of microlocal sheaves, which generalize local systems, and 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 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 B. There is a corresponding triangle for D. Finally, we prove that B and D are diffeomorphic, the diffeomorphism carries the weight filtration on the cohomology of B to the perverse Leray filtration on the cohomology of D, and all these structures are compatible with the deletion-contraction triangles.
- Subjects
COMPLEX manifolds; RIEMANN surfaces; FINITE fields; DIFFEOMORPHISMS; COHOMOLOGY theory; POLYNOMIALS
- Publication
Journal of the European Mathematical Society (EMS Publishing), 2024, Vol 26, Issue 7, p2565
- ISSN
1435-9855
- Publication type
Article
- DOI
10.4171/JEMS/1369