Volume 15, issue 6 (2015)

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The $L^2$–Alexander torsion is symmetric

Jérôme Dubois, Stefan Friedl and Wolfgang Lück

Algebraic & Geometric Topology 15 (2015) 3599–3612
Bibliography
1 F Ben Aribi, The $L^2$–Alexander invariant detects the unknot, C. R. Math. Acad. Sci. Paris 351 (2013) 215 MR3089681
2 F Ben Aribi, The $L^2$–Alexander invariant detects the unknot, C. R. Math. Acad. Sci. Paris 351 (2013) 215 MR3089681
3 T D Cochran, Noncommutative knot theory, Algebr. Geom. Topol. 4 (2004) 347 MR2077670
4 J Dubois, S Friedl, W Lück, The $L^2$–Alexander torsion of $3$–manifolds, preprint (2014) arXiv:1410.6918
5 J Dubois, S Friedl, W Lück, Three flavors of twisted knot invariants, preprint (2014) arXiv:1410.6924
6 J Dubois, C Wegner, $L^2$–Alexander invariant for torus knots, C. R. Math. Acad. Sci. Paris 348 (2010) 1185 MR2738924
7 J Dubois, C Wegner, Weighted $L^2$–invariants and applications to knot theory, Commun. Contemp. Math. 17 (2015) 1450010, 29 MR3291974
8 G Elek, E Szabó, Hyperlinearity, essentially free actions and $L^2$–invariants. The sofic property, Math. Ann. 332 (2005) 421 MR2178069
9 S Friedl, T Kim, T Kitayama, Poincaré duality and degrees of twisted Alexander polynomials, Indiana Univ. Math. J. 61 (2012) 147 MR3029395
10 S L Harvey, Higher-order polynomial invariants of $3$–manifolds giving lower bounds for the Thurston norm, Topology 44 (2005) 895 MR2153977
11 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
12 W Li, W Zhang, An $L^2$–Alexander–Conway invariant for knots and the volume conjecture, from: "Differential geometry and physics" (editors M L Ge, W Zhang), Nankai Tracts Math. 10, World Sci. Publ. (2006) 303 MR2327174
13 W Li, W Zhang, An $L^2$–Alexander invariant for knots, Commun. Contemp. Math. 8 (2006) 167 MR2219611
14 W Lück, $L^2$–invariants: Theory and applications to geometry and $K$–theory, Ergeb. Math. Grenzgeb. 44, Springer (2002) MR1926649
15 J R Munkres, Elements of algebraic topology, Addison-Wesley Publishing Company (1984) MR755006
16 W P Thurston, A norm for the homology of $3$–manifolds, Mem. Amer. Math. Soc. 339, Amer. Math. Soc. (1986) MR823443
17 V G Turaev, Euler structures, nonsingular vector fields, and Reidemeister-type torsions, Izv. Akad. Nauk SSSR Ser. Mat. 53 (1989) 607, 672 MR1013714
18 V G Turaev, Introduction to combinatorial torsions, Birkhäuser, Basel (2001) MR1809561
19 V G Turaev, Torsions of $3$–dimensional manifolds, Progress in Mathematics 208, Birkhäuser, Basel (2002) MR1958479
20 M Wada, Twisted Alexander polynomial for finitely presentable groups, Topology 33 (1994) 241 MR1273784