2024/05/23 by Allison H. Moore, Moore, Allison H., Nicola Tarasca +1 · 2 citations
Computer Science · Mathematics · #17B22 (Secondary) #57K16 #57K31 (Primary) #Algebraic Geometry (math.AG) #Computational Geometry and Mesh Generation #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Quantum Algebra (math.QA) #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2405.14972
openalex publication_date 2024/05/23 · openalex created_date 2024/05/28 · openalex updated_date 2026/07/28
We study formal series which are invariants of plumbed 3-manifolds twisted by root lattices. These series extend the BPS q-series \widehatZ(q) recently defined in Gukov-Pei-Putrov-Vafa, Gukov-Manolescu, Park, and further refined in Ri. We show that the series \widehatZ(q) is unique in an appropriate sense and decomposes as the average of related series which are themselves invariant under the five Neumann moves amongst plumbing trees. Explicit computations are presented in the case of Brieskorn spheres and a non-Seifert manifold.