#### Volume 12, issue 3 (2012)

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Exponential growth of torsion in abelian coverings

### Jean Raimbault

Algebraic & Geometric Topology 12 (2012) 1331–1372
##### Bibliography
 1 N Bergeron, A Venkatesh, The asymptotic growth of torsion homology for arithmetic groups, to appear in J. Inst. Math. Jussieu arXiv:1004.1083 2 J C Cha, S Friedl, T Kim, The cobordism group of homology cylinders, Compos. Math. 147 (2011) 914 MR2801405 3 B Clair, K Whyte, Growth of Betti numbers, Topology 42 (2003) 1125 MR1978050 4 G Everest, T Ward, Heights of polynomials and entropy in algebraic dynamics, Universitext, Springer (1999) MR1700272 5 F González-Acuña, H Short, Cyclic branched coverings of knots and homology spheres, Rev. Mat. Univ. Complut. Madrid 4 (1991) 97 MR1142552 6 C M Gordon, Knots whose branched cyclic coverings have periodic homology, Trans. Amer. Math. Soc. 168 (1972) 357 MR0295327 7 A Hatcher, Algebraic topology, Cambridge Univ. Press (2002) MR1867354 8 J Hempel, 3–Manifolds, Ann. of Math. Studies 86, Princeton Univ. Press (1976) MR0415619 9 E Kowalski, The large sieve and its applications, Cambridge Tracts in Mathematics 175, Cambridge Univ. Press (2008) MR2426239 10 M Lackenby, Finite covering spaces of 3–manifolds, from: "Proceedings of the International Congress of Mathematicians Volume II", Hindustan Book Agency (2010) 1042 MR2827831 11 T Y Lam, Serre's problem on projective modules, Springer Monographs in Mathematics, Springer (2006) MR2235330 12 W M Lawton, A problem of Boyd concerning geometric means of polynomials, J. Number Theory 16 (1983) 356 MR707608 13 T Le, Homology torsion growth and Mahler measure arXiv:1010.4199 14 W B R Lickorish, An introduction to knot theory, Graduate Texts in Mathematics 175, Springer (1997) MR1472978 15 P Linnell, W Lück, R Sauer, The limit of $\mathbb{F}_p$–Betti numbers of a tower of finite covers with amenable fundamental groups, Proc. Amer. Math. Soc. 139 (2011) 421 MR2736326 16 W Lück, Approximating $L^2$–invariants by their finite-dimensional analogues, Geom. Funct. Anal. 4 (1994) 455 MR1280122 17 W Lück, $L^2$–invariants: theory and applications to geometry and $K$–theory, Ergeb. Math. Grenzgeb. 44, Springer (2002) MR1926649 18 J P Mayberry, K Murasugi, Torsion-groups of abelian coverings of links, Trans. Amer. Math. Soc. 271 (1982) 143 MR648083 19 J Porti, Mayberry–Murasugi's formula for links in homology 3–spheres, Proc. Amer. Math. Soc. 132 (2004) 3423 MR2073320 20 R Riley, Growth of order of homology of cyclic branched covers of knots, Bull. London Math. Soc. 22 (1990) 287 MR1041145 21 A Schinzel, Polynomials with special regard to reducibility, Encyclopedia of Mathematics and its Applications 77, Cambridge Univ. Press (2000) MR1770638 22 K Schmidt, Dynamical systems of algebraic origin, Progress in Mathematics 128, Birkhäuser (1995) MR1345152 23 J P Serre, Local algebra, Springer Monographs in Mathematics, Springer (2000) MR1771925 24 D S Silver, S G Williams, Mahler measure, links and homology growth, Topology 41 (2002) 979 MR1923995 25 D S Silver, S G Williams, Torsion numbers of augmented groups with applications to knots and links, Enseign. Math. 48 (2002) 317 MR1955605 26 D S Silver, S G Williams, Dynamics of twisted Alexander invariants, Topology Appl. 156 (2009) 2795 MR2556037 27 V Turaev, Introduction to combinatorial torsions, Lectures in Mathematics ETH Zürich, Birkhäuser (2001) MR1809561