Research ArticleNo Access

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

Faculty of Mathematics, Kyushu University, 744, Motooka, Nishi-ku, Fukuoka 819-0395, Japan

E-mail Address: murakami.yuya.896@m.kyushu-u.ac.jp

E-mail Address: imaiburngermany@outlook.jp

https://doi.org/10.1142/S0218216524500354Cited by:0 (Source: Crossref)

Abstract

Gukov–Pei–Putrov–Vafa conjectured the existence of $q$ -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 $3$ -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.

Keywords:

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