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Twisting Kuperberg invariants via Fox calculus and Reidemeister torsion

Daniel López Neumann

Algebraic & Geometric Topology 22 (2022) 2419–2466
Bibliography
1 J W Alexander, Topological invariants of knots and links, Trans. Amer. Math. Soc. 30 (1928) 275 MR1501429
2 N Andruskiewitsch, P Etingof, S Gelaki, Triangular Hopf algebras with the Chevalley property, Michigan Math. J. 49 (2001) 277 MR1852304
3 C Blanchet, F Costantino, N Geer, B Patureau-Mirand, Nonsemisimple TQFTs, Reidemeister torsion and Kashaev’s invariants, Adv. Math. 301 (2016) 1 MR3539369
4 L Chang, S X Cui, On two invariants of three manifolds from Hopf algebras, Adv. Math. 351 (2019) 621 MR3954041
5 Q Chen, S Kuppum, P Srinivasan, On the relation between the WRT invariant and the Hennings invariant, Math. Proc. Cambridge Philos. Soc. 146 (2009) 151 MR2461874
6 F Costantino, N Geer, B Patureau-Mirand, V Turaev, Kuperberg and Turaev–Viro invariants in unimodular categories, Pacific J. Math. 306 (2020) 421 MR4129407
7 P Etingof, S Gelaki, D Nikshych, V Ostrik, Tensor categories, 205, Amer. Math. Soc. (2015) MR3242743
8 S Friedl, A Juhász, J Rasmussen, The decategorification of sutured Floer homology, J. Topol. 4 (2011) 431 MR2805998
9 S Friedl, S Vidussi, A survey of twisted Alexander polynomials, from: "The mathematics of knots" (editors M Banagl, D Vogel), Contrib. Math. Comput. Sci. 1, Springer (2011) 45 MR2777847
10 S Friedl, S Vidussi, Twisted Alexander polynomials detect fibered 3–manifolds, Ann. of Math. 173 (2011) 1587 MR2800721
11 S Friedl, S Vidussi, The Thurston norm and twisted Alexander polynomials, J. Reine Angew. Math. 707 (2015) 87 MR3403454
12 D Gabai, Foliations and the topology of 3–manifolds, J. Differential Geom. 18 (1983) 445 MR723813
13 M Hennings, Invariants of links and 3–manifolds obtained from Hopf algebras, J. London Math. Soc. 54 (1996) 594 MR1413901
14 V F R Jones, A polynomial invariant for knots via von Neumann algebras, Bull. Amer. Math. Soc. 12 (1985) 103 MR766964
15 A Juhász, Holomorphic discs and sutured manifolds, Algebr. Geom. Topol. 6 (2006) 1429 MR2253454
16 A Juhász, The sutured Floer homology polytope, Geom. Topol. 14 (2010) 1303 MR2653728
17 A Juhász, D Thurston, I Zemke, Naturality and mapping class groups in Heegaard Floer homology, 1338, Amer. Math. Soc. (2021) MR4337438
18 R Kashaev, A Virelizier, Generalized Kuperberg invariants of 3–manifolds, Algebr. Geom. Topol. 19 (2019) 2575 MR4023323
19 P Kirk, C Livingston, Twisted Alexander invariants, Reidemeister torsion, and Casson–Gordon invariants, Topology 38 (1999) 635 MR1670420
20 P Kirk, C Livingston, Twisted knot polynomials: inversion, mutation and concordance, Topology 38 (1999) 663 MR1670424
21 G Kuperberg, Involutory Hopf algebras and 3–manifold invariants, Internat. J. Math. 2 (1991) 41 MR1082836
22 G Kuperberg, Noninvolutory Hopf algebras and 3–manifold invariants, Duke Math. J. 84 (1996) 83 MR1394749
23 R G Larson, D E Radford, Finite-dimensional cosemisimple Hopf algebras in characteristic 0 are semisimple, J. Algebra 117 (1988) 267 MR957441
24 R G Larson, D E Radford, Semisimple cosemisimple Hopf algebras, Amer. J. Math. 110 (1988) 187 MR926744
25 X S Lin, Representations of knot groups and twisted Alexander polynomials, Acta Math. Sin. (Engl. Ser.) 17 (2001) 361 MR1852950
26 D López Neumann, Kuperberg invariants for balanced sutured 3–manifolds, Canad. J. Math. 73 (2021) 1698 MR4350558
27 C McPhail-Snyder, Holonomy invariants of links and nonabelian Reidemeister torsion, Quantum Topol. 13 (2022) 55 MR4404798
28 J Murakami, The multivariable Alexander polynomial and a one-parameter family of representations of 𝒰q(𝔰l(2,ℂ )) at q2 = − 1 , from: "Quantum groups" (editor P P Kulish), Lecture Notes in Math. 1510, Springer (1992) 350 MR1183500
29 P Ozsváth, Z Szabó, Holomorphic disks and topological invariants for closed three-manifolds, Ann. of Math. 159 (2004) 1027 MR2113019
30 J Porti, Reidemeister torsion, hyperbolic three-manifolds, and character varieties, from: "Handbook of group actions, IV" (editors L Ji, A Papadopoulos, S T Yau), Adv. Lect. Math. (ALM) 41, International (2018) 447 MR3888692
31 D E Radford, The group of automorphisms of a semisimple Hopf algebra over a field of characteristic 0 is finite, Amer. J. Math. 112 (1990) 331 MR1047302
32 D E Radford, Hopf algebras, 49, World Sci. (2012) MR2894855
33 K Reidemeister, Homotopieringe und Linsenräume, Abh. Math. Sem. Univ. Hamburg 11 (1935) 102 MR3069647
34 N Reshetikhin, Quantum supergroups, from: "Quantum field theory, statistical mechanics, quantum groups and topology" (editors T Curtright, L Mezincescu, R Nepomechie), World Sci. (1992) 264 MR1223142
35 N Y Reshetikhin, V G Turaev, Ribbon graphs and their invariants derived from quantum groups, Comm. Math. Phys. 127 (1990) 1 MR1036112
36 N Reshetikhin, V G Turaev, Invariants of 3–manifolds via link polynomials and quantum groups, Invent. Math. 103 (1991) 547 MR1091619
37 L Rozansky, H Saleur, Quantum field theory for the multi-variable Alexander–Conway polynomial, Nuclear Phys. B 376 (1992) 461 MR1170953
38 A Sartori, The Alexander polynomial as quantum invariant of links, Ark. Mat. 53 (2015) 177 MR3319619
39 V G Turaev, Quantum invariants of knots and 3–manifolds, 18, de Gruyter (1994) MR1292673
40 V Turaev, Homotopy field theory in dimension 3 and crossed group-categories, preprint (2000) arXiv:math/0005291
41 V Turaev, Introduction to combinatorial torsions, Birkhäuser (2001) MR1809561
42 V Turaev, Homotopy quantum field theory, 10, Eur. Math. Soc. (2010) MR2674592
43 A Virelizier, Hopf group-coalgebras, J. Pure Appl. Algebra 171 (2002) 75 MR1903398
44 A Virelizier, Involutory Hopf group-coalgebras and flat bundles over 3–manifolds, Fund. Math. 188 (2005) 241 MR2191947
45 M Wada, Twisted Alexander polynomial for finitely presentable groups, Topology 33 (1994) 241 MR1273784
46 E Witten, Quantum field theory and the Jones polynomial, Comm. Math. Phys. 121 (1989) 351 MR990772