Geometry & Topology Volume 19, issue 4 (2015)

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ISSN (electronic): 1364-0380

ISSN (print): 1465-3060

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Generating the Johnson filtration

Thomas Church and Andrew Putman

Geometry & Topology 19 (2015) 2217–2255

DOI: 10.2140/gt.2015.19.2217

Bibliography

1	H Bass, J Milnor, J P Serre, Solution of the congruence subgroup problem for $\mathrm{ SL}_{n}(n\geq 3)$ and $\mathrm{Sp}_{2n}(n\geq 2)$, Inst. Hautes Études Sci. Publ. Math. (1967) 59 MR0244257
2	M Bestvina, K U Bux, D Margalit, Dimension of the Torelli group for $\mathrm{Out}(F_n)$, Invent. Math. 170 (2007) 1 MR2336078
3	J S Birman, Mapping class groups and their relationship to braid groups, Comm. Pure Appl. Math. 22 (1969) 213 MR0243519
4	N Bourbaki, Lie groups and Lie algebras, Chapters 1–3, Elements of Math. (Berlin), Springer (1989) MR979493
5	T Church, J S Ellenberg, B Farb, FI–modules and stability for representations of symmetric groups, Duke Math. J. 164 (2015) 1833 MR3357185
6	T Church, J S Ellenberg, B Farb, R Nagpal, FI–modules over Noetherian rings, Geom. Topol. 18 (2014) 2951 MR3285226
7	J Cooper, Two $\mathrm{mod}$-$p$ Johnson filtrations, J. Topol. Anal. 7 (2015) 309
8	M Day, A Putman, The complex of partial bases for $F_n$ and finite generation of the Torelli subgroup of $\mathrm{Aut}(F_n)$, Geom. Dedicata 164 (2013) 139 MR3054621
9	N Enomoto, T Satoh, On the derivation algebra of the free Lie algebra and trace maps, Algebr. Geom. Topol. 11 (2011) 2861 MR2846914
10	E Fadell, L Neuwirth, Configuration spaces, Math. Scand. 10 (1962) 111 MR0141126
11	B Farb, D Margalit, A primer on mapping class groups, Princeton Math. Series 49, Princeton Univ. Press (2012) MR2850125
12	S Garoufalidis, J Levine, Finite type $3$–manifold invariants and the structure of the Torelli group, I, Invent. Math. 131 (1998) 541 MR1614551
13	A Hatcher, D Margalit, Generating the Torelli group, Enseign. Math. 58 (2012) 165 MR2985015
14	N V Ivanov, J D McCarthy, On injective homomorphisms between Teichmüller modular groups, I, Invent. Math. 135 (1999) 425 MR1666775
15	D L Johnson, Homeomorphisms of a surface which act trivially on homology, Proc. Amer. Math. Soc. 75 (1979) 119 MR529227
16	D L Johnson, An abelian quotient of the mapping class group $\mathcal{ I}_{g}$, Math. Ann. 249 (1980) 225 MR579103
17	D L Johnson, The structure of the Torelli group, I: A finite set of generators for $\mathcal{I}$, Ann. of Math. 118 (1983) 423 MR727699
18	D L Johnson, A survey of the Torelli group, from: "Low-dimensional topology" (editor S J Lomonaco Jr.), Contemp. Math. 20, Amer. Math. Soc. (1983) 165 MR718141
19	D L Johnson, The structure of the Torelli group, II: A characterization of the group generated by twists on bounding curves, Topology 24 (1985) 113 MR793178
20	D L Johnson, The structure of the Torelli group, III: The abelianization of $\mathcal{T}$, Topology 24 (1985) 127 MR793179
21	W B R Lickorish, A finite set of generators for the homeotopy group of a $2$–manifold, Proc. Cambridge Philos. Soc. 60 (1964) 769 MR0171269
22	W Magnus, Über $n$–dimensionale Gittertransformationen, Acta Math. 64 (1935) 353 MR1555401
23	M Matsumoto, Introduction to arithmetic mapping class groups, from: "Moduli spaces of Riemann surfaces" (editors B Farb, R Hain, E Looijenga), IAS/Park City Math. Ser. 20, Amer. Math. Soc. (2013) 319 MR3114689
24	D Mumford, Abelian quotients of the Teichmüller modular group, J. Analyse Math. 18 (1967) 227 MR0219543
25	M Newman, J R Smart, Symplectic modulary groups, Acta Arith 9 (1964) 83 MR0162862
26	B Perron, Filtration de Johnson et groupe de Torelli modulo $p$, $p$ premier, C. R. Math. Acad. Sci. Paris 346 (2008) 667 MR2423275
27	J Powell, Two theorems on the mapping class group of a surface, Proc. Amer. Math. Soc. 68 (1978) 347 MR0494115
28	A Putman, Cutting and pasting in the Torelli group, Geom. Topol. 11 (2007) 829 MR2302503
29	A Putman, Small generating sets for the Torelli group, Geom. Topol. 16 (2012) 111 MR2872579
30	A Putman, Stability in the homology of congruence subgroups, Invent. Math. (2015)
31	T Satoh, On the Johnson filtration of the basis-conjugating automorphism group of a free group, Michigan Math. J. 61 (2012) 87 MR2904002
32	T Satoh, On the lower central series of the $\mathrm{IA}$–automorphism group of a free group, J. Pure Appl. Algebra 216 (2012) 709 MR2864772
33	J Stallings, Homology and central series of groups, J. Algebra 2 (1965) 170 MR0175956
34	B Sury, T N Venkataramana, Generators for all principal congruence subgroups of $\mathrm{ SL}(n,\mathbb{Z})$ with $n\geq 3$, Proc. Amer. Math. Soc. 122 (1994) 355 MR1239806
35	J Tits, Systèmes générateurs de groupes de congruence, C. R. Acad. Sci. Paris Sér. A-B 283 (1976) MR0424966
36	E Witt, Treue Darstellungen Liescher Ringe, J. Reine Angew. Math. 177 (1937) 152
37	H Zassenhaus, Ein Verfahren, jeder endlichenp–Gruppe einen Lie–Ring mit der Charakteristikp zuzuordnen, Abh. Math. Sem. Univ. Hamburg 13 (1939) 200 MR3069703