TY - JOUR
T1 - Resurgence analysis of quantum invariants of Seifert fibered homology spheres
AU - Andersen, Jørgen Ellegaard
AU - Mistegård, William Elbæk
N1 - Funding Information:
We warmly thank S. Gukov for valuable discussions on the GPPV invariant . The first author was supported in part by the center of excellence grant ‘Center for Quantum Geometry of Moduli Spaces’ from the Danish National Research Foundation (DNRF95) and by the ERC‐Synergy grant ‘ReNewQuantum’. The second author received funding from the European Union's Horizon 2020 research and innovation program under the Marie Skłodowska‐Curie grant agreement no. 754411.
Publisher Copyright:
© 2022 The Authors. Journal of the London Mathematical Society is copyright © London Mathematical Society.
PY - 2022/3
Y1 - 2022/3
N2 - For a Seifert fibered homology sphere 푋, we show that
the 푞-series invariant Ẑ 0(푋; 푞), introduced by Gukov–
Pei–Putrov–Vafa, is a resummation of the Ohtsuki series
Z0(푋). We show that for every even 푘 ∈ ℕ there exists
a full asymptotic expansion of Ẑ 0(푋; 푞) for 푞 tending to
푒2휋푖∕푘, and in particular that the limit Ẑ 0(푋; 푒2휋푖∕푘) exists
and is equal to the Witten–Reshetikhin–Turaev quantum invariant 휏푘(푋). We show that the poles of the Borel
transform of Z0(푋) coincide with the classical complex
Chern–Simons values, which we further show classifies
the corresponding components of the moduli space of
flat SL(2, ℂ)-connections.
AB - For a Seifert fibered homology sphere 푋, we show that
the 푞-series invariant Ẑ 0(푋; 푞), introduced by Gukov–
Pei–Putrov–Vafa, is a resummation of the Ohtsuki series
Z0(푋). We show that for every even 푘 ∈ ℕ there exists
a full asymptotic expansion of Ẑ 0(푋; 푞) for 푞 tending to
푒2휋푖∕푘, and in particular that the limit Ẑ 0(푋; 푒2휋푖∕푘) exists
and is equal to the Witten–Reshetikhin–Turaev quantum invariant 휏푘(푋). We show that the poles of the Borel
transform of Z0(푋) coincide with the classical complex
Chern–Simons values, which we further show classifies
the corresponding components of the moduli space of
flat SL(2, ℂ)-connections.
U2 - 10.1112/jlms.12506
DO - 10.1112/jlms.12506
M3 - Journal article
AN - SCOPUS:85124598813
SN - 0024-6107
VL - 105
SP - 709
EP - 764
JO - Journal of the London Mathematical Society
JF - Journal of the London Mathematical Society
IS - 2
ER -