English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Some years ago, it was conjectured by the first author that the Chern-Simonsperturbation theory of a 3-manifold at the trivial flat connection is aresurgent power series. We describe completely the resurgent structure of theabove series (including the location of the singularities and their Stokesconstants) in the case of a hyperbolic knot complement in terms of an extendedsquare matrix of $(x,q)$-series whose rows are indexed by the boundaryparabolic $\text{SL}_2(\mathbb{C})$-flat connections, including the trivialone. We use our extended matrix to describe the Stokes constants of the aboveseries, to define explicitly their Borel transform and to identify it withstate-integrals. Along the way, we use our matrix to give an analytic extensionof the Kashaev invariant and of the colored Jones polynomial and to completethe matrix valued holomorphic quantum modular forms as well as to give an exactversion of the refined quantum modularity conjecture of Zagier and the firstauthor. Finally, our matrix provides an extension of the 3D-index in a sectorof the trivial flat connection. We illustrate our definitions, theorems,numerical calculations and conjectures with the two simplest hyperbolic knots.

Resurgence of Chern-Simons theory at the trivial flat connection