Volume 11, issue 5 (2011)

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

Volume 24
Issue 5, 2389–2970
Issue 4, 1809–2387
Issue 3, 1225–1808
Issue 2, 595–1223
Issue 1, 1–594

Volume 23, 9 issues

Volume 22, 8 issues

Volume 21, 7 issues

Volume 20, 7 issues

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
Editorial Interests
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Author Index
To Appear
 
Other MSP Journals
On the derivation algebra of the free Lie algebra and trace maps

Naoya Enomoto and Takao Satoh

Algebraic & Geometric Topology 11 (2011) 2861–2901
Bibliography
1 S Andreadakis, On the automorphisms of free groups and free nilpotent groups, Proc. London Math. Soc. $(3)$ 15 (1965) 239 MR0188307
2 S Andreadakis, Generators for $\mathrm{Aut} G,$ $G$ free nilpotent, Arch. Math. $($Basel$)$ 42 (1984) 296 MR753347
3 S Bachmuth, Induced automorphisms of free groups and free metabelian groups, Trans. Amer. Math. Soc. 122 (1966) 1 MR0190212
4 J S Birman, Braids, links, and mapping class groups, Annals of Math. Studies 82, Princeton Univ. Press (1974) MR0375281
5 N Bourbaki, Lie groups and Lie algebras. Chapters 1–3, Elements of Math., Springer (1989) MR979493
6 R M Bryant, C K Gupta, Automorphism groups of free nilpotent groups, Arch. Math. $($Basel$)$ 52 (1989) 313 MR998406
7 K T Chen, Integration in free groups, Ann. of Math. $(2)$ 54 (1951) 147 MR0042414
8 F R Cohen, J Pakianathan, On automorphism groups of free groups and their nilpotent quotients, preprint
9 F R Cohen, J Pakianathan, On subgroups of the automorphism group of a free group and associated graded Lie algebras, preprint
10 H S M Coxeter, W O J Moser, Generators and relations for discrete groups, Ergebnisse der Math. und ihrer Grenzgebiete 14, Springer (1972) MR0349820
11 B Farb, Automorphisms of $F_n$ which act trivially on homology, in preparation
12 A M Garsia, Combinatorics of the free Lie algebra and the symmetric group, from: "Analysis, et cetera" (editors P H Rabinowitz, E Zehnder), Academic Press (1990) 309 MR1039352
13 A V Goryaga, Generating elements of the group of automorphisms of a free nilpotent group, Algebra i Logika 15 (1976) 458, 488 MR0450415
14 R Hain, Infinitesimal presentations of the Torelli groups, J. Amer. Math. Soc. 10 (1997) 597 MR1431828
15 D Johnson, An abelian quotient of the mapping class group $\mathcal{I}_{g}$, Math. Ann. 249 (1980) 225 MR579103
16 D Johnson, The structure of the Torelli group—III: The abelianization of $\mathscr T$, Topology 24 (1985) 127 MR793179
17 M D Kassabov, On the automorphism tower of free nilpotent groups, PhD thesis, Yale University (2003) arXiv:math/0311488
18 N Kawazumi, Cohomological aspects of Magnus expansions arXiv:math.GT/0505497
19 A A Kljačko, Lie elements in a tensor algebra, Sibirsk. Mat. Ž. 15 (1974) 1296, 1430 MR0371961
20 K Koike, On the decomposition of tensor products of the representations of the classical groups: by means of the universal characters, Adv. Math. 74 (1989) 57 MR991410
21 M Kontsevich, Formal (non)commutative symplectic geometry, from: "The Gel$'`$fand Mathematical Seminars, 1990–1992" (editors L Corwin, I Gel′‘fand, J Lepowsky), Birkhäuser (1993) 173 MR1247289
22 M Kontsevich, Feynman diagrams and low-dimensional topology, from: "First European Congress of Mathematics, Vol. II (Paris, 1992)" (editors A Joseph, F Mignot, F Murat, B Prum, R Rentschler), Progr. Math. 120, Birkhäuser (1994) 97 MR1341841
23 W Kraśkiewicz, J Weyman, Algebra of coinvariants and the action of a Coxeter element, Bayreuth. Math. Schr. (2001) 265 MR1867283
24 S Krstić, J McCool, The non-finite presentability of $\mathrm{IA}(F_3)$ and $\mathrm{GL}_2(\mathbf{Z}[t,t^{-1}])$, Invent. Math. 129 (1997) 595 MR1465336
25 W Lin, Presentations of the automorphism groups of free nilpotent groups, Comm. Algebra 24 (1996) 3403 MR1405261
26 W Magnus, Über $n$–dimensionale Gittertransformationen, Acta Math. 64 (1935) 353 MR1555401
27 S Morita, Families of Jacobian manifolds and characteristic classes of surface bundles. I, Ann. Inst. Fourier (Grenoble) 39 (1989) 777 MR1030850
28 S Morita, Abelian quotients of subgroups of the mapping class group of surfaces, Duke Math. J. 70 (1993) 699 MR1224104
29 S Morita, The extension of Johnson's homomorphism from the Torelli group to the mapping class group, Invent. Math. 111 (1993) 197 MR1193604
30 S Morita, Structure of the mapping class groups of surfaces: a survey and a prospect, from: "Proceedings of the Kirbyfest (Berkeley, CA, 1998)" (editors J Hass, M Scharlemann), Geom. Topol. Monogr. 2 (1999) 349 MR1734418
31 S Morita, Cohomological structure of the mapping class group and beyond, from: "Problems on mapping class groups and related topics" (editor B Farb), Proc. Sympos. Pure Math. 74, Amer. Math. Soc. (2006) 329 MR2264550
32 J Nielsen, Die Isomorphismengruppe der freien Gruppen, Math. Ann. 91 (1924) 169 MR1512188
33 A Pettet, The Johnson homomorphism and the second cohomology of $\mathrm{IA}_n$, Algebr. Geom. Topol. 5 (2005) 725 MR2153110
34 C Reutenauer, Free Lie algebras, London Math. Soc. Monogr. New Series 7, Oxford Science Publ., The Clarendon Press, Oxford Univ. Press (1993) MR1231799
35 T Satoh, New obstructions for the surjectivity of the Johnson homomorphism of the automorphism group of a free group, J. London Math. Soc. $(2)$ 74 (2006) 341 MR2269583
36 T Satoh, Twisted first homology groups of the automorphism group of a free group, J. Pure Appl. Algebra 204 (2006) 334 MR2184815
37 T Satoh, The cokernel of the Johnson homomorphisms of the automorphism group of a free metabelian group, Trans. Amer. Math. Soc. 361 (2009) 2085 MR2465830
38 T Satoh, On the lower central series of the IA-automorphism group of a free group, preprint (2009)
39 T Satoh, On the fourth Johnson homomorphism of the automorphism group of a free group, J. Algebra 323 (2010) 3182 MR2639972
40 T Satoh, A reduction of the target of the Johnson homomorphisms of the automorphism group of a free group, Trans. Amer. Math. Soc. 363 (2011) 1631 MR2737281
41 E Witt, Treue Darstellung Liescher Ringe, J. Reine Angew. Math. 177 (1937) 152