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Cutting and pasting in the Torelli subgroup of $\operatorname{Out}(F_{n})$

Jacob Landgraf

Algebraic & Geometric Topology 25 (2025) 1–38
Bibliography
1 S Andreadakis, On the automorphisms of free groups and free nilpotent groups, Proc. Lond. Math. Soc. 15 (1965) 239 MR188307
2 M A Armstrong, On the fundamental group of an orbit space, Proc. Cambridge Philos. Soc. 61 (1965) 639 MR187244
3 S Bachmuth, Induced automorphisms of free groups and free metabelian groups, Trans. Amer. Math. Soc. 122 (1966) 1 MR190212
4 J E Banks, The Birman exact sequence for 3-manifolds, Bull. Lond. Math. Soc. 49 (2017) 604 MR3725483
5 M Bestvina, K U Bux, D Margalit, Dimension of the Torelli group for Out(Fn), Invent. Math. 170 (2007) 1 MR2336078
6 T Brendle, N Broaddus, A Putman, The mapping class group of connect sums of S2 × S1, Trans. Amer. Math. Soc. 376 (2023) 2557 MR4557874
7 M R Bridson, K Vogtmann, Automorphism groups of free groups, surface groups and free abelian groups, from: "Problems on mapping class groups and related topics", Proc. Sympos. Pure Math. 74, Amer. Math. Soc. (2006) 301 MR2264548
8 T Church, B Farb, A Putman, Integrality in the Steinberg module and the top-dimensional cohomology of SLn𝒪K, Amer. J. Math. 141 (2019) 1375 MR4011804
9 M Day, A Putman, A Birman exact sequence for Aut(Fn), Adv. Math. 231 (2012) 243 MR2935388
10 M Day, A Putman, The complex of partial bases for Fn and finite generation of the Torelli subgroup of Aut(Fn), Geom. Dedicata 164 (2013) 139 MR3054621
11 M Day, A Putman, A Birman exact sequence for the Torelli subgroup of Aut(Fn), Int. J. Algebra Comput. 26 (2016) 585 MR3506351
12 B Farb, D Margalit, A primer on mapping class groups, 49, Princeton Univ. Press (2012) MR2850125
13 A Hatcher, Homological stability for automorphism groups of free groups, Comment. Math. Helv. 70 (1995) 39 MR1314940
14 A Hatcher, N Wahl, Stabilization for the automorphisms of free groups with boundaries, Geom. Topol. 9 (2005) 1295 MR2174267
15 A Hatcher, N Wahl, Stabilization for mapping class groups of 3-manifolds, Duke Math. J. 155 (2010) 205 MR2736166
16 C A Jensen, N Wahl, Automorphisms of free groups with boundaries, Algebr. Geom. Topol. 4 (2004) 543 MR2077676
17 D Johnson, The structure of the Torelli group, III : The abelianization of 𝒯 , Topology 24 (1985) 127 MR793179
18 F Laudenbach, Sur les 2-sphères d’une variété de dimension 3, Ann. of Math. 97 (1973) 57 MR314054
19 F Laudenbach, Topologie de la dimension trois: homotopie et isotopie, 12, Soc. Math. France (1974) MR356056
20 H Maazen, Homology stability for the general linear group, PhD thesis, Utrecht University (1951)
21 W Magnus, Über n-dimensionale Gittertransformationen, Acta Math. 64 (1935) 353 MR1555401
22 A Putman, Cutting and pasting in the Torelli group, Geom. Topol. 11 (2007) 829 MR2302503
23 A Putman, Obtaining presentations from group actions without making choices, Algebr. Geom. Topol. 11 (2011) 1737 MR2821439
24 A Putman, The commutator subgroups of free groups and surface groups, Enseign. Math. 68 (2022) 389 MR4452428
25 W Tomaszewski, A basis of Bachmuth type in the commutator subgroup of a free group, Canad. Math. Bull. 46 (2003) 299 MR1981684
26 N Wahl, From mapping class groups to automorphism groups of free groups, J. Lond. Math. Soc. 72 (2005) 510 MR2156667