Geometry & Topology Volume 21, issue 5 (2017)

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On the second homology group of the Torelli subgroup of $\mathrm{Aut}(F_n)$

Matthew Day and Andrew Putman

Geometry & Topology 21 (2017) 2851–2896

DOI: 10.2140/gt.2017.21.2851

Bibliography

1	S Andreadakis, On the automorphisms of free groups and free nilpotent groups, Proc. London Math. Soc. 15 (1965) 239 MR0188307
2	O Baker, The Jacobian map on outer space, PhD thesis, Cornell University (2011)
3	L Bartholdi, Endomorphic presentations of branch groups, J. Algebra 268 (2003) 419 MR2009317
4	M Bestvina, K U Bux, D Margalit, Dimension of the Torelli group for Out(F_n), Invent. Math. 170 (2007) 1 MR2336078
5	S K Boldsen, M Hauge Dollerup, Towards representation stability for the second homology of the Torelli group, Geom. Topol. 16 (2012) 1725 MR2967062
6	A Borel, Density properties for certain subgroups of semi-simple groups without compact components, Ann. of Math. 72 (1960) 179 MR0123639
7	A Borel, Stable real cohomology of arithmetic groups, Ann. Sci. École Norm. Sup. 7 (1974) 235 MR0387496
8	A Borel, Stable real cohomology of arithmetic groups, II, from: "Manifolds and Lie groups" (editors S Murakami, J Hano, K Okamoto, A Morimoto, H Ozeki), Progr. Math. 14, Birkhäuser (1981) 21 MR642850
9	T Brendle, D Margalit, A Putman, Generators for the hyperelliptic Torelli group and the kernel of the Burau representation at t = −1, Invent. Math. 200 (2015) 263 MR3323579
10	K S Brown, Cohomology of groups, 87, Springer (1994) MR1324339
11	T Church, B Farb, Parameterized Abel–Jacobi maps and abelian cycles in the Torelli group, J. Topol. 5 (2012) 15 MR2897048
12	T Church, B Farb, Representation theory and homological stability, Adv. Math. 245 (2013) 250 MR3084430
13	T Church, A Putman, The codimension-one cohomology of SL_nℤ, Geom. Topol. 21 (2017) 999 MR3626596
14	F Cohen, J Pakianathan, On automorphism groups of free groups and their nilpotent quotients, in preparation
15	M Day, A Putman, A Birman exact sequence for Aut(F_n), Adv. Math. 231 (2012) 243 MR2935388
16	M Day, A Putman, The complex of partial bases for F_n and finite generation of the Torelli subgroup of Aut(F_n), Geom. Dedicata 164 (2013) 139 MR3054621
17	M Day, A Putman, A Birman exact sequence for the Torelli subgroup of Aut(F_n), Internat. J. Algebra Comput. 26 (2016) 585 MR3506351
18	B Farb, Automorphisms of F_n which act trivially on homology, in preparation
19	S Galatius, Stable homology of automorphism groups of free groups, Ann. of Math. 173 (2011) 705 MR2784914
20	A Hatcher, K Vogtmann, Cerf theory for graphs, J. London Math. Soc. 58 (1998) 633 MR1678155
21	A Hatcher, N Wahl, Stabilization for mapping class groups of 3–manifolds, Duke Math. J. 155 (2010) 205 MR2736166
22	D Johnson, An abelian quotient of the mapping class group ℐ_g, Math. Ann. 249 (1980) 225 MR579103
23	N Kawazumi, Cohomological aspects of Magnus expansions, preprint (2005) arXiv:math/0505497
24	S Krstić, J McCool, The non-finite presentability of IA(F₃) and GL₂(ℤ[t,t⁻¹]), Invent. Math. 129 (1997) 595 MR1465336
25	R C Lyndon, P E Schupp, Combinatorial group theory, 89, Springer (1977) MR0577064
26	W Magnus, Über n–dimensionale Gittertransformationen, Acta Math. 64 (1935) 353 MR1555401
27	J Nielsen, Die Isomorphismen der allgemeinen, unendlichen Gruppe mit zwei Erzeugenden, Math. Ann. 78 (1917) 385 MR1511907
28	A Putman, An infinite presentation of the Torelli group, Geom. Funct. Anal. 19 (2009) 591 MR2545251
29	A Putman, Obtaining presentations from group actions without making choices, Algebr. Geom. Topol. 11 (2011) 1737 MR2821439
30	A Putman, The second rational homology group of the moduli space of curves with level structures, Adv. Math. 229 (2012) 1205 MR2855091
31	T Satoh, The abelianization of the congruence IA–automorphism group of a free group, Math. Proc. Cambridge Philos. Soc. 142 (2007) 239 MR2314598
32	T Satoh, A survey of the Johnson homomorphisms of the automorphism groups of free groups and related topics, preprint (2012) arXiv:1204.0876