Campbell Wheeler

activity

20242026

collaborators

6 papers

math.GT2026

A lift of the colored Jones polynomial of a knot

Stavros Garoufalidis, Campbell Wheeler

Habiro lifted the Witten-Reshetikhin-Turaev invariant of an integer homology 3-sphere (a complex-valued function on the set of complex roots of unity) to an element of the Habiro r…

math.NT2025

The Habiro ring of a number field

Stavros Garoufalidis, Peter Scholze, Campbell Wheeler +1

We introduce the Habiro ring of a number field $K$ and modules over it graded by $K_{3} (K)$ . Elements of these modules are collections of power series at each compl…

math.AG2025

Explicit classes in Habiro cohomology

Stavros Garoufalidis, Campbell Wheeler

We propose a cycle description of the Habiro cohomology of a smooth variety $X$ over the spectrum $B$ of an Ã©tale $Z [I^»]$ -algebra and construct explicit nontrivial cycles using ei…

math.NT2025

Resurgence, Habiro elements and strange identities

Samuel Crew, Veronica Fantini, Ankush Goswami +2

We prove resurgence properties for the Borel transform of a formal power series associated to elements in the Habiro ring that come from radial limits of partial theta series via s…

math.GT2025

Quantum Modularity for a Closed Hyperbolic 3-Manifold

Campbell Wheeler

This paper proves quantum modularity of both functions from $Q$ and $q$ -series associated to the closed manifold obtained by $- \frac{1}{2}$ surgery on the figure-eight kno…

math.GT2024

Summability for State Integrals of hyperbolic knots

Veronica Fantini, Campbell Wheeler

We prove conjectures of Garoufalidis-Gu-MariÃ±o that perturbative series associated with the hyperbolic knots $4_{1}$ and $5_{2}$ are resurgent and Borel summable. In the process, we g…