Work

Witten–Reshetikhin–Turaev invariants and indefinite false theta functions for plumbing indefinite H-graphs

Year: 2024

Type: article

Abstract: Gukov–Pei–Putrov–Vafa conjectured the existence of [Formula: see text]-series whose radial limits are Witten–Reshetikhin–Turaev invariants and called them homological blocks. For weakly negative definite plumbed 3-manifolds, Gukov–Pei–Putrov–Vafa and Gukov–Manolescu constructed homological blocks. In this paper, we construct indefinite false theta functions which are candidates of homological blocks for some plumbed [Formula: see text]-manifolds which are not weakly negative definite. Moreover we prove that, for the Poincaré homology sphere, our indefinite false theta function coincides with the original homological block.

Source: Journal of Knot Theory and Its Ramifications

DOI: 10.1142/s0218216524500354

Author: Yuya Murakami

Institution: Kyushu University

Language: English

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Japan Society for the Promotion of Science

Award: 量子モジュラー形式の基礎的研究