Algebraic & Geometric Topology Volume 18, issue 5 (2018)

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The profinite completions of knot groups determine the Alexander polynomials

Jun Ueki

Algebraic & Geometric Topology 18 (2018) 3013–3030

DOI: 10.2140/agt.2018.18.3013

Bibliography

1	M Artin, B Mazur, On periodic points, Ann. of Math. 81 (1965) 82 MR0176482
2	M Asada, On Galois groups of abelian extensions over maximal cyclotomic fields, Tohoku Math. J. 60 (2008) 135 MR2419040
3	M F Atiyah, I G Macdonald, Introduction to commutative algebra, Addison-Wesley (1969) MR0242802
4	N Bergeron, A Venkatesh, The asymptotic growth of torsion homology for arithmetic groups, J. Inst. Math. Jussieu 12 (2013) 391 MR3028790
5	M Boileau, S Boyer, On the Tits alternative for PD(3) groups, preprint (2017) arXiv:1710.10670
6	M Boileau, S Friedl, The profinite completion of 3–manifold groups, fiberedness and the Thurston norm, preprint (2015) arXiv:1505.07799
7	M Boileau, S Friedl, Grothendieck rigidity of 3–manifold groups, preprint (2017) arXiv:1710.02746
8	O Braunling, Torsion homology growth beyond asymptotics, preprint (2017) arXiv:1702.06243
9	M R Bridson, F J Grunewald, Grothendieck’s problems concerning profinite completions and representations of groups, Ann. of Math. 160 (2004) 359 MR2119723
10	M R Bridson, A W Reid, Profinite rigidity, fibering, and the figure-eight knot, preprint (2015) arXiv:1505.07886
11	M R Bridson, A W Reid, H Wilton, Profinite rigidity and surface bundles over the circle, Bull. Lond. Math. Soc. 49 (2017) 831 MR3742450
12	R H Fox, Free differential calculus, III : Subgroups, Ann. of Math. 64 (1956) 407 MR0095876
13	R H Fox, Covering spaces with singularities, from: "A symposium in honor of S Lefschetz" (editors R H Fox, D C Spencer, A W Tucker), Princeton Univ. Press (1957) 243 MR0123298
14	D Fried, Cyclic resultants of reciprocal polynomials, from: "Holomorphic dynamics" (editors X Gómez-Mont, J Seade, A Verjovsky), Lecture Notes in Math. 1345, Springer (1988) 124 MR980956
15	S Friedl, S Vidussi, Twisted Alexander polynomials detect fibered 3–manifolds, Ann. of Math. 173 (2011) 1587 MR2800721
16	L Funar, Torus bundles not distinguished by TQFT invariants, Geom. Topol. 17 (2013) 2289 MR3109869
17	F Q Gouvêa, p–adic numbers : an introduction, Springer (1997) MR1488696
18	A Grothendieck, Représentations linéaires et compactification profinie des groupes discrets, Manuscripta Math. 2 (1970) 375 MR0262386
19	J Hempel, Residual finiteness for 3–manifolds, from: "Combinatorial group theory and topology" (editors S M Gersten, J R Stallings), Ann. of Math. Stud. 111, Princeton Univ. Press (1987) 379 MR895623
20	J Hempel, Some 3–manifold groups with the same finite quotients, preprint (2014) arXiv:1409.3509
21	C J Hillar, Cyclic resultants, J. Symbolic Comput. 39 (2005) 653 MR2167674
22	A Jaikin-Zapirain, Recognition of being fibred for compact 3–manifolds, preprint (2017)
23	U Jannsen, Continuous étale cohomology, Math. Ann. 280 (1988) 207 MR929536
24	T Kitayama, M Morishita, R Tange, Y Terashima, On certain L–functions for deformations of knot group representations, Trans. Amer. Math. Soc. 370 (2018) 3171 MR3766846
25	K Kodama, M Sakuma, Symmetry groups of prime knots up to 10 crossings, from: "Knots 90" (editor A Kawauchi), de Gruyter (1992) 323 MR1177431
26	T Le, Growth of homology torsion in finite coverings and hyperbolic volume, preprint (2014) arXiv:1412.7758
27	D D Long, A W Reid, Grothendieck’s problem for 3–manifold groups, Groups Geom. Dyn. 5 (2011) 479 MR2782181
28	W Lück, Survey on L²–torsion, talk slides (2015)
29	B Mazur, Remarks on the Alexander polynomial, unpublished note (1963/1964)
30	B Mazur, Primes, knots and Po, lecture notes for the conference “Geometry, topology and group theory” in honor of the 80th birthday of Valentin Poenaru (2012)
31	S Mochizuki, Topics in absolute anabelian geometry, III : Global reconstruction algorithms, J. Math. Sci. Univ. Tokyo 22 (2015) 939 MR3445958
32	M Morishita, Knots and primes: an introduction to arithmetic topology, Springer (2012) MR2905431
33	M Morishita, Y Takakura, Y Terashima, J Ueki, On the universal deformations for SL₂–representations of knot groups, Tohoku Math. J. 69 (2017) 67 MR3640015
34	G Perelman, The entropy formula for the Ricci flow and its geometric applications, preprint (2002) arXiv:math/0211159
35	G Perelman, Ricci flow with surgery on three-manifolds, preprint (2003) arXiv:math/0303109
36	G Perelman, Finite extinction time for the solutions to the Ricci flow on certain three-manifolds, preprint (2003) arXiv:math/0307245
37	K A Perko Jr., On the classification of knots, Proc. Amer. Math. Soc. 45 (1974) 262 MR0353294
38	V P Platonov, O I Tavgen’, On the Grothendieck problem of profinite completions of groups, Dokl. Akad. Nauk SSSR 288 (1986) 1054 MR852649
39	L Ribes, P Zalesskii, Profinite groups, 40, Springer (2010) MR2599132
40	D Rolfsen, Knots and links, 7, Publish or Perish (1990) MR1277811
41	R Tange, Fox formulas for twisted Alexander invariants associated to representations of knot groups over rings of S–integers, J. Knot Theory Ramifications 27 (2018) 1850033, 15 MR3795397
42	J Ueki, p–adic Mahler measure and ℤ–covers of links, preprint (2017) arXiv:1702.03819
43	C Weber, Sur une formule de R H Fox concernant l’homologie des revêtements cycliques, Enseign. Math. 25 (1979) 261 MR570312
44	G Wilkes, Profinite rigidity for Seifert fibre spaces, Geom. Dedicata 188 (2017) 141 MR3639628
45	G Wilkes, Relative cohomology theory for profinite groups, preprint (2017) arXiv:1710.00730
46	G Wilkes, Profinite completions, cohomology and JSJ decompositions of compact 3–manifolds, preprint (2018) arXiv:1802.09282
47	G Wilkes, Profinite rigidity of graph manifolds and JSJ decompositions of 3–manifolds, J. Algebra 502 (2018) 538 MR3774902
48	G Wilkes, Profinite rigidity of graph manifolds, II: Knots and mapping classes, preprint (2018) arXiv:1801.06386
49	H Wilton, P Zalesskii, Profinite properties of graph manifolds, Geom. Dedicata 147 (2010) 29 MR2660565
50	H Wilton, P Zalesskii, Distinguishing geometries using finite quotients, Geom. Topol. 21 (2017) 345 MR3608716
51	H Wilton, P Zalesskii, Profinite detection of 3–manifold decompositions, preprint (2017) arXiv:1703.03701