2024/10/14 by Louisa Liles, Liles, Louisa
Mathematics · Physics and Astronomy · #11F37 #57K31 #Advanced Algebra and Geometry #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Nonlinear Waves and Solitons
paper · pdf · doi:10.48550/arxiv.2410.10561
openalex publication_date 2024/10/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Gukov, Pei, Putrov, and Vafa developed a q-series invariant of negative definite plumbed 3-manifolds with spinc structures, building on earlier work of Lawrence and Zagier. This was recently generalized to an an infinite family of two-variable (t,q)-series invariants by Akhmechet, Johnson, and Krushkal (AJK). We calculate one such series for all Seifert manifolds with b1=0. These results extend a previous theorem of Liles and McSpirit to any number of exceptional fibers and the Reduction Theorem of Gukov, Svoboda, and Katzarkov to the two-variable case. As a consequence, a previous result of Liles and McSpirit on modularity properties and radial limits is enhanced to a larger family of manifolds. We also calculate the infinite collection of (t,q)-series invariants for three infinite families of manifolds, finding mixed modularity properties for one such family.