On Hempel pairs and Turaev--Viro invariants

Surface bundles arising from periodic mapping classes may sometimes have non-isomorphic, but profinitely isomorphic fundamental groups. Pairs of this kind have been discovered by Hempel. This paper exhibits examples of nontrivial Hempel pairs where the mapping tori can be distinguished by some Turaev--Viro invariants, and also examples where they cannot be distinguished by any Turaev--Viro invariants.

[1]  A. Reid.  PROFINITE RIGIDITY , 2019, Proceedings of the International Congress of Mathematicians (ICM 2018).

[2]  Efstratia Kalfagianni,et al.  Quantum representations and monodromies of fibered links , 2017, Advances in Mathematics.

[3]  Tian Yang,et al.  Turaev–Viro invariants, colored Jones polynomials, and volume , 2017, Quantum Topology.

[4]  J. Hempel.  Some 3-manifold groups with the same finite quotients , 2014, 1409.3509.

[5]  Matthias Aschenbrenner,et al.  3-Manifold Groups , 2012, 1205.0202.

[6]  J. Andersen,et al.  The Witten-Reshetikhin-Turaev invariants of finite order mapping tori II , 2011, 1107.1813.

[7]  L. Funar.  Torus bundles not distinguished by TQFT invariants , 2011, 1101.0509.

[8]  Taiji Taniguchi.  The Turaev-Viro Invariants of All Orientable Closed Seifert Fibered Manifolds , 2007 .

[9]  S. Nikitin.  On 3-manifolds , 2005, Graduate Studies in Mathematics.

[10]  S. K. Hansen.  Reshetikhin{Turaev invariants of Seifert 3{manifolds and a rational surgery formula , 2001, math/0111057.

[11]  Albert Schwarz,et al.  Topological quantum field theories , 2000, hep-th/0011260.

[12]  L. Rozansky,et al.  Witten–Reshetikhin–Turaev Invariants of¶Seifert Manifolds , 1999 .

[13]  M. V. Sokolov,et al.  Which lens spaces are distinguished by Turaev-Viro invariants , 1997 .

[14]  M. Sokolov.  The Turaev-viro Invariant for 3-Manifolds is a Sum of Three Invariants , 1996, Canadian Mathematical Bulletin.

[15]  Justin Roberts,et al.  Skein theory and Turaev-Viro invariants , 1995 .

[16]  N. Habegger,et al.  Topological Auantum Field Theories derived from the Kauffman bracket , 1995 .

[17]  V. Turaev.  Quantum Invariants of Knots and 3-Manifolds , 1994, hep-th/9409028.

[18]  N. Habegger,et al.  Three-manifold invariants derived from the Kauffman bracket , 1992 .

[19]  Vladimir Turaev,et al.  State sum invariants of 3 manifolds and quantum 6j symbols , 1992 .

[20]  Paul Melvin,et al.  The 3-manifold invariants of Witten and Reshetikhin-Turaev for sl(2, C) , 1991 .

[21]  Vladimir Turaev,et al.  Invariants of 3-manifolds via link polynomials and quantum groups , 1991 .

[22]  Edward Witten,et al.  Quantum field theory and the Jones polynomial , 1989 .

[23]  Hongbin Sun,et al.  Toward and after virtual specialization in $3$-manifold topology , 2020, Surveys in Differential Geometry.

[24]  Marina Daecher,et al.  Introduction To Cyclotomic Fields , 2016 .

[25]  Peter Orlik,et al.  On Seifert-manifolds , 1966 .