Volume 8, issue 2 (2008)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 20
Issue 3, 1073–1600
Issue 2, 531–1072
Issue 1, 1–529

Volume 19, 7 issues

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Editorial Board
Subscriptions
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Ethics Statement
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Author Index
To Appear
 
Other MSP Journals
The Magnus representation and higher-order Alexander invariants for homology cobordisms of surfaces

Takuya Sakasai

Algebraic & Geometric Topology 8 (2008) 803–848
Bibliography
1 S Andreadakis, On the automorphisms of free groups and free nilpotent groups, Proc. London Math. Soc. $(3)$ 15 (1965) 239 MR0188307
2 J S Birman, Braids, links, and mapping class groups, Annals of Math. Studies 82, Princeton University Press (1974) MR0375281
3 J Cha, Injectivity theorems and algebraic closures of groups with coefficients arXiv:math.GT/0609408
4 T D Cochran, Noncommutative knot theory, Algebr. Geom. Topol. 4 (2004) 347 MR2077670
5 T D Cochran, K E Orr, P Teichner, Knot concordance, Whitney towers and $L^2$–signatures, Ann. of Math. $(2)$ 157 (2003) 433 MR1973052
6 P M Cohn, Skew fields. Theory of general division rings, Encyclopedia of Math. and its Applications 57, Cambridge University Press (1995) MR1349108
7 R H Fox, Free differential calculus. II. The isomorphism problem of groups, Ann. of Math. $(2)$ 59 (1954) 196 MR0062125
8 S Friedl, Reidemeister torsion, the Thurston norm and Harvey's invariants, Pacific J. Math. 230 (2007) 271 MR2309160
9 S Garoufalidis, J Levine, Tree-level invariants of three-manifolds, Massey products and the Johnson homomorphism, from: "Graphs and patterns in mathematics and theoretical physics", Proc. Sympos. Pure Math. 73, Amer. Math. Soc. (2005) 173 MR2131016
10 M Goussarov, Finite type invariants and $n$–equivalence of $3$–manifolds, C. R. Acad. Sci. Paris Sér. I Math. 329 (1999) 517 MR1715131
11 K Habiro, Claspers and finite type invariants of links, Geom. Topol. 4 (2000) 1 MR1735632
12 S L Harvey, Higher-order polynomial invariants of $3$–manifolds giving lower bounds for the Thurston norm, Topology 44 (2005) 895 MR2153977
13 S L Harvey, Monotonicity of degrees of generalized Alexander polynomials of groups and $3$–manifolds, Math. Proc. Cambridge Philos. Soc. 140 (2006) 431 MR2225642
14 S L Harvey, S Friedl, Non-commutative multivariable Reidemester torsion and the Thurston norm, Algebr. Geom. Topol. 7 (2007) 755 MR2308963
15 N Kawazumi, Cohomological aspects of Magnus expansions arXiv:math.GT/0505497
16 P Kirk, C Livingston, Z Wang, The Gassner representation for string links, Commun. Contemp. Math. 3 (2001) 87 MR1820015
17 J Y Le Dimet, Enlacements d'intervalles et représentation de Gassner, Comment. Math. Helv. 67 (1992) 306 MR1161287
18 J Y Le Dimet, Enlacements d'intervalles et torsion de Whitehead, Bull. Soc. Math. France 129 (2001) 215 MR1871296
19 J Levine, Knot modules. I, Trans. Amer. Math. Soc. 229 (1977) 1 MR0461518
20 J Levine, Algebraic closure of groups, from: "Combinatorial group theory (College Park, MD, 1988)", Contemp. Math. 109, Amer. Math. Soc. (1990) 99 MR1076380
21 J Levine, Homology cylinders: an enlargement of the mapping class group, Algebr. Geom. Topol. 1 (2001) 243 MR1823501
22 W Magnus, Über $n$–dimensionale Gittertransformationen, Acta Math. 64 (1935) 353 MR1555401
23 J Milnor, Whitehead torsion, Bull. Amer. Math. Soc. 72 (1966) 358 MR0196736
24 S Morita, Abelian quotients of subgroups of the mapping class group of surfaces, Duke Math. J. 70 (1993) 699 MR1224104
25 J Nielsen, Die Isomorphismen der allgemeinen, unendlichen Gruppe mit zwei Erzeugenden, Math. Ann. 78 (1964) 385 MR1511907
26 D S Passman, The algebraic structure of group rings, Pure and Applied Mathematics, Wiley-Interscience (1977) MR470211
27 J Rosenberg, Algebraic $K$–theory and its applications, Graduate Texts in Math. 147, Springer (1994) MR1282290
28 T Sakasai, Homology cylinders and the acyclic closure of a free group, Algebr. Geom. Topol. 6 (2006) 603 MR2220691
29 T Sakasai, The symplecticity of the Magnus representation for homology cobordisms of surfaces, Bull. Austral. Math. Soc. 76 (2007) 421 MR2374173
30 J Stallings, Homology and central series of groups, J. Algebra 2 (1965) 170 MR0175956
31 V Turaev, Introduction to combinatorial torsions, Lectures in Math. ETH Zürich, Birkhäuser Verlag (2001) MR1809561