Algebraic & Geometric Topology Volume 12, issue 3 (2012)

Download this article
	For screen
	For printing

Recent Issues

The Journal

Submission Guidelines

Submission Page

Ethics Statement

ISSN (electronic): 1472-2739

ISSN (print): 1472-2747

To Appear

Other MSP Journals

Exponential growth of torsion in abelian coverings

Jean Raimbault

Algebraic & Geometric Topology 12 (2012) 1331–1372

DOI: 10.2140/agt.2012.12.1331

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