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

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.

17 pages, 5 figures, 1 table

Cited by in corpus (1)

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