Algebraic & Geometric Topology Volume 6, issue 2 (2006)

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the Journal

Editorial Board

Subscriptions

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN 1472-2739 (online)

ISSN 1472-2747 (print)

Author Index

To Appear

Other MSP Journals

Euclidean Mahler measure and twisted links

Daniel S Silver, Alexander Stoimenow and Susan G Williams

Algebraic & Geometric Topology 6 (2006) 581–602

DOI: 10.2140/agt.2006.6.581

Bibliography

1	S Bhatty, Mahler measure and the Alexander polynomial of pretzel links, Undergraduate honors thesis, University of South Alabama (2004)
2	D W Boyd, Speculations concerning the range of Mahler’s measure, Canad. Math. Bull. 24 (1981) 453 MR644535
3	J W Brown, R V Churchill, Complex variables and applications, McGraw-Hill Book Co. (1984) MR730937
4	P J Callahan, J C Dean, J R Weeks, The simplest hyperbolic knots, J. Knot Theory Ramifications 8 (1999) 279 MR1691433
5	A Champanerkar, I Kofman, On the Mahler measure of Jones polynomials under twisting, Algebr. Geom. Topol. 5 (2005) 1 MR2135542
6	A Champanerkar, I Kofman, E Patterson, The next simplest hyperbolic knots, J. Knot Theory Ramifications 13 (2004) 965 MR2101238
7	P R Cromwell, Homogeneous links, J. London Math. Soc. (2) 39 (1989) 535 MR1002465
8	O Dasbach, X S Lin, A volume-ish theorem for the Jones polynomial of alternating knots, arXiv:math.GT/0403448
9	G Everest, T Ward, Heights of polynomials and entropy in algebraic dynamics, , Springer London Ltd. (1999) MR1700272
10	C M Gordon, Toroidal Dehn surgeries on knots in lens spaces, Math. Proc. Cambridge Philos. Soc. 125 (1999) 433 MR1656809
11	E Hironaka, The Lehmer polynomial and pretzel links, Canad. Math. Bull. 44 (2001) 440 MR1863636
12	V F R Jones, Hecke algebra representations of braid groups and link polynomials, Ann. of Math. (2) 126 (1987) 335 MR908150
13	E Kalfagianni, Alexander polynomial, finite type invariants and volume of hyperbolic knots, Algebr. Geom. Topol. 4 (2004) 1111 MR2113898
14	K Kodama, Knot, a program for computing knot invariants
15	M Lackenby, The volume of hyperbolic alternating link complements, Proc. London Math. Soc. (3) 88 (2004) 204 MR2018964
16	D H Lehmer, Factorization of certain cyclotomic functions, Ann. of Math. (2) 34 (1933) 461 MR1503118
17	D A Lind, T Ward, Automorphisms of solenoids and p–adic entropy, Ergodic Theory Dynam. Systems 8 (1988) 411 MR961739
18	K Mahler, On some inequalities for polynomials in several variables, J. London Math. Soc. 37 (1962) 341 MR0138593
19	K Murasugi, On alternating knots, Osaka Math. J. 12 (1960) 277 MR0137107
20	K Murasugi, Non-amphicheirality of the special alternating links, Proc. Amer. Math. Soc. 13 (1962) 771 MR0142116
21	K Murasugi, J H Przytycki, The skein polynomial of a planar star product of two links, Math. Proc. Cambridge Philos. Soc. 106 (1989) 273 MR1002540
22	K Murasugi, A Stoimenow, The Alexander polynomial of planar even valence graphs, Adv. in Appl. Math. 31 (2003) 440 MR2001624
23	H Seifert, Über das Geschlecht von Knoten, Math. Ann. 110 (1935) 571 MR1512955
24	D S Silver, W Whitten, Hyperbolic covering knots, Algebr. Geom. Topol. 5 (2005) 1451 MR2186104
25	D S Silver, S G Williams, Lehmer’s question, knots and surface dynamics, arXiv:math.GT/0509068
26	D S Silver, S G Williams, Mahler measure, links and homology growth, Topology 41 (2002) 979 MR1923995
27	D S Silver, S G Williams, Mahler measure of Alexander polynomials, J. London Math. Soc. (2) 69 (2004) 767 MR2050045
28	A Stoimenow, Alexander polynomials and hyperbolic volume of arborescent links, preprint
29	A Stoimenow, A property of the skein polynomial with an application to contact geometry, arXiv:math.GT/0008126
30	A Stoimenow, The Jones polynomial, genus and weak genus of a knot, Ann. Fac. Sci. Toulouse Math. (6) 8 (1999) 677 MR1815161
31	A Stoimenow, On the coefficients of the link polynomials, Manuscripta Math. 110 (2003) 203 MR1962535