Volume 13, issue 4 (2013)

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Growth of regulators in finite abelian coverings

Thang T Q Lê

Algebraic & Geometric Topology 13 (2013) 2383–2404
Bibliography
1 N Bergeron, A Venkatesh, The asymptotic growth of torsion homology for arithmetic groups, J. Inst. Math. Jussieu 12 (2013) 391 MR3028790
2 D Bertrand, Duality on tori and multiplicative dependence relations, J. Austral. Math. Soc. Ser. A 62 (1997) 198 MR1433209
3 B Clair, K Whyte, Growth of Betti numbers, Topology 42 (2003) 1125 MR1978050
4 G Elek, Abelian coverings, J. Funct. Anal. 141 (1996) 365 MR1418511
5 S Friedl, N Jackson, Approximations to the volume of hyperbolic knots arXiv:1102.3742
6 F González-Acuña, H Short, Cyclic branched coverings of knots and homology spheres, Rev. Mat. Univ. Complut. Madrid 4 (1991) 97 MR1142552
7 J A Hillman, M Sakuma, On the homology of finite abelian coverings of links, Canad. Math. Bull. 40 (1997) 309 MR1464839
8 M Laurent, Équations diophantiennes exponentielles, Invent. Math. 78 (1984) 299 MR767195
9 T T Q Lê, Homology torsion growth and Mahler measure, to appear in Comment. Math. Helv. arXiv:1010.4199
10 T T Q Lê, Hyperbolic volume, Mahler measure, and homology growth, talk at Columbia University (2009)
11 W Lück, Approximating $L^2$-invariants by their finite-dimensional analogues, Geom. Funct. Anal. 4 (1994) 455 MR1280122
12 W Lück, $L^2$-invariants: theory and applications to geometry and $K$-theory, Ergeb. Math. Grenzgeb. 44, Springer (2002) MR1926649
13 J P Mayberry, K Murasugi, Torsion-groups of abelian coverings of links, Trans. Amer. Math. Soc. 271 (1982) 143 MR648083
14 J W Milnor, Infinite cyclic coverings, from: "Conference on the Topology of Manifolds" (editor J G Hocking), Prindle, Weber & Schmidt (1968) 115 MR0242163
15 J Porti, Mayberry–Murasugi's formula for links in homology 3-spheres, Proc. Amer. Math. Soc. 132 (2004) 3423 MR2073320
16 J Raimbault, Exponential growth of torsion in abelian coverings, Algebr. Geom. Topol. 12 (2012) 1331 MR2966689
17 R Riley, Growth of order of homology of cyclic branched covers of knots, Bull. London Math. Soc. 22 (1990) 287 MR1041145
18 W Schmidt, Heights of points on subvarieties of $\mathbf{G}^n_m$, from: "Number theory" (editors V K Murty, M Waldschmidt), Contemp. Math. 210, Amer. Math. Soc. (1998) 97 MR1478487
19 J P Serre, Linear representations of finite groups, Graduate Texts in Mathematics 42, Springer (1977) MR0450380
20 D S Silver, S G Williams, Mahler measure, links and homology growth, Topology 41 (2002) 979 MR1923995
21 V Turaev, Introduction to combinatorial torsions, Lectures in Mathematics ETH Zürich, Birkhäuser (2001) MR1809561