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Root lattices and series valued invariants of plumbed 3-manifolds
Geometry/Topology| Speaker: | Allison Moore, Virginia Commonwealth University |
| Related Webpage: | https://allisonhmoore.github.io/ |
| Location: | 1147 MSB |
| Start time: | Fri, May 22 2026, 4:10PM |
Description
Given a reduced plumbing tree and a spin-c structure, I will discuss how to construct a plumbed 3-manifold invariant in the form of a Laurent series twisted by a root lattice. Such a series is invariant under the Neumann moves on plumbing trees and the action of the Weyl group. These series-valued invariants generalize the Z-hat series of Gukov-Pei-Putrov-Vafa, Gukov-Manolescu, Park and Ri. They are motivated by the study of the WRT invariants, and the work of Akhmechet-Johnson-Krushkal which found connections with lattice cohomology. There is a multivariable generalization of our root lattice-twisted series for knot complements that satisfies gluing and splitting formulas. Time permitting, I will discuss the form of this series for specific manifolds, for example Brieskorn spheres. This is joint work with N. Tarasca.