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Alexander and Thurston norms, and the Bieri–Neumann–Strebel invariants for free-by-cyclic groups

Florian Funke and Dawid Kielak

Geometry & Topology 22 (2018) 2647–2696
Bibliography
1 J W Alexander, Topological invariants of knots and links, Trans. Amer. Math. Soc. 30 (1928) 275 MR1501429
2 L Bartholdi, Amenability of groups is characterized by Myhill’s theorem, with an appendix by D Kielak, preprint (2016) arXiv:1605.09133
3 M Bestvina, M Feighn, M Handel, The Tits alternative for Out(Fn), I : Dynamics of exponentially-growing automorphisms, Ann. of Math. 151 (2000) 517 MR1765705
4 R Bieri, W D Neumann, R Strebel, A geometric invariant of discrete groups, Invent. Math. 90 (1987) 451 MR914846
5 C H Cashen, G Levitt, Mapping tori of free group automorphisms, and the Bieri–Neumann–Strebel invariant of graphs of groups, J. Group Theory 19 (2016) 191 MR3466593
6 J C Cha, S Friedl, F Funke, The Grothendieck group of polytopes and norms, Münster J. Math. 10 (2017) 75 MR3624102
7 M Clay, 2–torsion of free-by-cyclic groups, Q. J. Math. 68 (2017) 617 MR3667215
8 P M Cohn, Free ideal rings and localization in general rings, 3, Cambridge Univ. Press (2006) MR2246388
9 W Dicks, P Menal, The group rings that are semifirs, J. London Math. Soc. 19 (1979) 288 MR533328
10 J Dieudonné, Les déterminants sur un corps non commutatif, Bull. Soc. Math. France 71 (1943) 27 MR0012273
11 J Dubois, S Friedl, W Lück, The L2–Alexander torsion of 3–manifolds, preprint (2014) arXiv:1410.6918
12 N M Dunfield, Alexander and Thurston norms of fibered 3–manifolds, Pacific J. Math. 200 (2001) 43 MR1863406
13 R H Fox, Free differential calculus, I : Derivation in the free group ring, Ann. of Math. 57 (1953) 547 MR0053938
14 S Friedl, W Lück, The L2–torsion function and the Thurston norm of 3–manifolds, preprint (2015) arXiv:1510.00264
15 S Friedl, W Lück, L2–Euler characteristics and the Thurston norm, preprint (2016) arXiv:1609.07805
16 S Friedl, W Lück, Universal L2–torsion, polytopes and applications to 3–manifolds, Proc. Lond. Math. Soc. 114 (2017) 1114 MR3661347
17 S Friedl, S Tillmann, Two-generator one-relator groups and marked polytopes, preprint (2015) arXiv:1501.03489
18 F Funke, The integral polytope group, preprint (2016) arXiv:1605.01217
19 F Funke, The L2–torsion polytope of amenable groups, preprint (2017) arXiv:1704.07164
20 R Geoghegan, M L Mihalik, M Sapir, D T Wise, Ascending HNN extensions of finitely generated free groups are Hopfian, Bull. London Math. Soc. 33 (2001) 292 MR1817768
21 M Hall Jr., Subgroups of finite index in free groups, Canadian J. Math. 1 (1949) 187 MR0028836
22 S L Harvey, Higher-order polynomial invariants of 3–manifolds giving lower bounds for the Thurston norm, Topology 44 (2005) 895 MR2153977
23 S L Harvey, Monotonicity of degrees of generalized Alexander polynomials of groups and 3–manifolds, Math. Proc. Cambridge Philos. Soc. 140 (2006) 431 MR2225642
24 S Harvey, S Friedl, Non-commutative multivariable Reidemester torsion and the Thurston norm, Algebr. Geom. Topol. 7 (2007) 755 MR2308963
25 G Higman, The units of group-rings, Proc. London Math. Soc. 46 (1940) 231 MR0002137
26 D H Kochloukova, Some Novikov rings that are von Neumann finite and knot-like groups, Comment. Math. Helv. 81 (2006) 931 MR2271229
27 P Linnell, W Lück, Localization, Whitehead groups, and the Atiyah conjecture, preprint (2016) arXiv:1602.06906
28 W Lück, L2–invariants : theory and applications to geometry and K–theory, 44, Springer (2002) MR1926649
29 W Lück, Twisting L2–invariants with finite-dimensional representations, preprint (2015) arXiv:1510.00057
30 W Lück, T Schick, L2–torsion of hyperbolic manifolds of finite volume, Geom. Funct. Anal. 9 (1999) 518 MR1708444
31 A I Mal’cev, On the embedding of group algebras in division algebras, Doklady Akad. Nauk SSSR 60 (1948) 1499 MR0025457
32 C T McMullen, The Alexander polynomial of a 3–manifold and the Thurston norm on cohomology, Ann. Sci. École Norm. Sup. 35 (2002) 153 MR1914929
33 B H Neumann, On ordered division rings, Trans. Amer. Math. Soc. 66 (1949) 202 MR0032593
34 J C Sikorav, Homologie de Novikov associée à une classe de cohomologie réelle de degré un, Thèse d’Etat, Universit’e Paris-Sud XI, Orsay (1987)
35 J R Silvester, Introduction to algebraic K–theory, Chapman & Hall (1981) MR629979
36 J R Stallings, Topology of finite graphs, Invent. Math. 71 (1983) 551 MR695906
37 R Strebel, Notes on the Sigma invariants, preprint (2012) arXiv:1204.0214
38 D Tamari, A refined classification of semi-groups leading to generalized polynomial rings with a generalized degree concept, from: "Proceedings of the International Congress of Mathematicians" (editors J C H Gerretsen, J d Groot), North-Holland (1957) 439
39 W P Thurston, A norm for the homology of 3–manifolds, Mem. Amer. Math. Soc. 339, Amer. Math. Soc. (1986) 99 MR823443
40 F Waldhausen, Algebraic K–theory of generalized free products, III, IV, Ann. of Math. 108 (1978) 205 MR0498808
41 C Wegner, The Farrell–Jones conjecture for virtually solvable groups, J. Topol. 8 (2015) 975 MR3431666