2023/06/26 by Louisa Liles, Liles, Louisa, Eleanor McSpirit +1 · 2 citations
Computer Science · Mathematics · #11F27 #11F37 #57K31 #Advanced Combinatorial Mathematics #FOS: Mathematics #Geometric Topology (math.GT) #Homotopy and Cohomology in Algebraic Topology #Number Theory (math.NT) #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2306.14765
openalex publication_date 2023/06/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
One of the first key examples of a quantum modular form, which unifies the Witten-Reshetikhin-Turaev (WRT) invariants of the Poincaré homology sphere, appears in work of Lawrence and Zagier. We show that the series they construct is one instance in an infinite family of quantum modular invariants of negative definite plumbed 3-manifolds whose radial limits toward roots of unity may be thought of as a deformation of the WRT invariants. We use a recently developed theory of Akhmechet, Johnson, and Krushkal (AJK) which extends lattice cohomology and BPS q-series of 3-manifolds. As part of this work, we provide the first calculation of the AJK series for an infinite family of 3-manifolds. Additionally, we introduce a separate but related infinite family of invariants which also exhibit quantum modularity properties.