Algebraic & Geometric Topology Volume 13, issue 4 (2013)

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ISSN (electronic): 1472-2739

ISSN (print): 1472-2747

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Growth of regulators in finite abelian coverings

Thang T Q Lê

Algebraic & Geometric Topology 13 (2013) 2383–2404

DOI: 10.2140/agt.2013.13.2383

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