Conjecture that recovered q-series are invariants for arbitrary plumbings

Let a plumbed 3-manifold be represented by an arbitrary, possibly non-reduced, plumbing, and let the associated (q,t)(q,t)-series be specialized by taking t1t\rightarrow 1 to obtain a recovered qq-series. Recovered q-series invariance conjecture. The recovered qq-series, obtained from the (q,t)(q,t)-series in the sense of t1t\rightarrow 1, is an invariant of 33-manifolds realized by arbitrary (i.e., possibly non-reduced) plumbings. This extends the proposed invariance beyond reduced plumbings; the claim is not established in the supplied text.

Sources & referencesView supporting material

Primary source

Song Jin Ri, “Refined and Generalized Z Invariants for Plumbed 3-Manifolds”, arXiv:2205.08197 (2023).

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