Algebraic & Geometric Topology Volume 26, issue 4 (2026)

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The rational abelianization of the Chillingworth subgroup of the mapping class group of a surface

Ryotaro Kosuge

Algebraic & Geometric Topology 26 (2026) 1465–1505

DOI: 10.2140/agt.2026.26.1465

Bibliography

1	M Asada, M Kaneko, On the automorphism group of some pro-l fundamental groups, from: "Galois representations and arithmetic algebraic geometry" (editor Y Ihara), Adv. Stud. Pure Math. 12, North-Holland, Amsterdam (1987) 137 MR948240
2	M Asada, H Nakamura, On graded quotient modules of mapping class groups of surfaces, Israel J. Math. 90 (1995) 93 MR1336318
3	J S Birman, Abelian quotients of the mapping class group of a 2-manifold, Bull. Amer. Math. Soc. 76 (1970) 147 MR249603
4	J S Birman, R Craggs, The μ-invariant of 3-manifolds and certain structural properties of the group of homeomorphisms of a closed, oriented 2-manifold, Trans. Amer. Math. Soc. 237 (1978) 283 MR482765
5	C Blanchet, M Palmer, A Shaukat, Heisenberg homology on surface configurations, (2025)
6	L R Childers, Simply intersecting pair maps in the mapping class group, J. Knot Theory Ramifications 21 (2012) 1250107 MR2969637
7	D R J Chillingworth, Winding numbers on surfaces, I, Math. Ann. 196 (1972) 218 MR300304
8	D R J Chillingworth, Winding numbers on surfaces, II, Math. Ann. 199 (1972) 131 MR321091
9	A Dimca, R Hain, S Papadima, The abelianization of the Johnson kernel, J. Eur. Math. Soc. 16 (2014) 805 MR3191977
10	C J Earle, Families of Riemann surfaces and Jacobi varieties, Ann. of Math. (2) 107 (1978) 255 MR499328
11	Q Faes, Triviality of the J₄-equivalence among homology 3-spheres, Trans. Amer. Math. Soc. 375 (2022) 6597 MR4474902
12	Q Faes, G Massuyeau, On the non-triviality of the torsion subgroup of the abelianized Johnson kernel, Annales de l’Institut Fourier 76 (2026) 425
13	W Fulton, J Harris, Representation theory : a first course, 129, Springer (1991) MR1153249
14	N Habegger, W Pitsch, Tree level Lie algebra structures of perturbative invariants, J. Knot Theory Ramifications 12 (2003) 333 MR1983089
15	R Hain, Infinitesimal presentations of the Torelli groups, J. Amer. Math. Soc. 10 (1997) 597 MR1431828
16	B Harris, Iterated integrals and cycles on algebraic manifolds, 7, World Sci. (2004) MR2063961
17	D Johnson, An abelian quotient of the mapping class group ℐ_g, Math. Ann. 249 (1980) 225 MR579103
18	D Johnson, A survey of the Torelli group, from: "Low-dimensional topology" (editor J Lomonaco Samuel J.), Contemp. Math. 20, Amer. Math. Soc. (1983) 165 MR718141
19	D Johnson, The structure of the Torelli group, III : The abelianization of ℐ, Topology 24 (1985) 127 MR793179
20	D Johnson, The structure of the Torelli group, II : A characterization of the group generated by twists on bounding curves, Topology 24 (1985) 113 MR793178
21	M Korkmaz, Low-dimensional homology groups of mapping class groups: a survey, Turkish J. Math. 26 (2002) 101 MR1892804
22	J P Labute, On the descending central series of groups with a single defining relation, J. Algebra 14 (1970) 16 MR251111
23	G Massuyeau, Infinitesimal Morita homomorphisms and the tree-level of the LMO invariant, Bull. Soc. Math. France 140 (2012) 101 MR2903772
24	W Meyer, Die Signatur von Flächenbündeln, Math. Ann. 201 (1973) 239 MR331382
25	S Morita, Casson’s invariant for homology 3-spheres and characteristic classes of surface bundles, I, Topology 28 (1989) 305 MR1014464
26	S Morita, Families of Jacobian manifolds and characteristic classes of surface bundles, I, Ann. Inst. Fourier (Grenoble) 39 (1989) 777 MR1030850
27	S Morita, Families of Jacobian manifolds and characteristic classes of surface bundles, II, Math. Proc. Cambridge Philos. Soc. 105 (1989) 79 MR966142
28	S Morita, On the structure of the Torelli group and the Casson invariant, Topology 30 (1991) 603 MR1133875
29	S Morita, Abelian quotients of subgroups of the mapping class group of surfaces, Duke Math. J. 70 (1993) 699 MR1224104
30	S Morita, The extension of Johnson’s homomorphism from the Torelli group to the mapping class group, Invent. Math. 111 (1993) 197 MR1193604
31	S Morita, A linear representation of the mapping class group of orientable surfaces and characteristic classes of surface bundles, from: "Topology and Teichmüller spaces" (editors S Kojima, Y Matsumoto, K Saito, M Seppälä), World Sci. (1996) 159 MR1659679
32	S Morita, Casson invariant, signature defect of framed manifolds and the secondary characteristic classes of surface bundles, J. Differential Geom. 47 (1997) 560 MR1617632
33	S Morita, Structure of the mapping class groups of surfaces : a survey and a prospect, from: "Proceedings of the Kirbyfest" (editors J Hass, M Scharlemann), Geom. Topol. Monogr. 2, Geom. Topol. Publ. (1999) 349 MR1734418
34	S Morita, T Sakasai, M Suzuki, Torelli group, Johnson kernel, and invariants of homology spheres, Quantum Topol. 11 (2020) 379 MR4118638
35	D Mumford, Abelian quotients of the Teichmüller modular group, J. Analyse Math. 18 (1967) 227 MR219543
36	J Powell, Two theorems on the mapping class group of a surface, Proc. Amer. Math. Soc. 68 (1978) 347 MR494115
37	T Sakasai, The Johnson homomorphism and the third rational cohomology group of the Torelli group, Topology Appl. 148 (2005) 83 MR2118957
38	T Sakasai, The second Johnson homomorphism and the second rational cohomology of the Johnson kernel, preprint (2006) arXiv:math/0601314
39	T Sakasai, The second Johnson homomorphism and the second rational cohomology of the Johnson kernel, Math. Proc. Cambridge Philos. Soc. 143 (2007) 627 MR2373963
40	T Sakasai, Johnson’s homomorphisms and the rational cohomology of subgroups of the mapping class group, from: "Groups of diffeomorphisms" (editors R Penner, D Kotschick, T Tsuboi, N Kawazumi, T Kitano, Y Mitsumatsu), Adv. Stud. Pure Math. 52, Math. Soc. Japan (2008) 93 MR2509707
41	R Trapp, A linear representation of the mapping class group ℳ and the theory of winding numbers, Topology Appl. 43 (1992) 47 MR1141372