Volume 12, issue 1 (2012)

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Lagrangian mapping class groups from a group homological point of view

Takuya Sakasai

Algebraic & Geometric Topology 12 (2012) 267–291
Bibliography
1 J E Andersen, A J Bene, J B Meilhan, R C Penner, Finite type invariants and fatgraphs, Adv. Math. 225 (2010) 2117 MR2680201
2 V I Arnol’d, The cohomology ring of the group of dyed braids, Mat. Zametki 5 (1969) 227 MR0242196
3 J S Birman, Braids, links, and mapping class groups, 82, Princeton Univ. Press (1974) MR0375281
4 J S Birman, On the equivalence of Heegaard splittings of closed, orientable 3–manifolds, from: "Knots, groups, and 3–manifolds (Papers dedicated to the memory of R. H. Fox)" (editor L P Neuwirth), Ann. of Math. Studies 84, Princeton Univ. Press (1975) 137 MR0375318
5 J S Birman, T E Brendle, N Broaddus, Calculating the image of the second Johnson–Morita representation, 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) 119 MR2509709
6 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 MR0482765
7 A Borel, Stable real cohomology of arithmetic groups II, from: "Manifolds and Lie groups (Notre Dame, Ind., 1980)" (editors S Murakami, J Hano, K Okamoto, A Morimoto, H Ozeki), Progr. Math. 14, Birkhäuser (1981) 21 MR642850
8 N Broaddus, B Farb, A Putman, Irreducible Sp–representations and subgroup distortion in the mapping class group, Comment. Math. Helv. 86 (2011) 537 MR2803852
9 K S Brown, Cohomology of groups, 87, Springer (1982) MR672956
10 D Cheptea, K Habiro, G Massuyeau, A functorial LMO invariant for Lagrangian cobordisms, Geom. Topol. 12 (2008) 1091 MR2403806
11 D Cheptea, T T Q Le, A TQFT associated to the LMO invariant of three-dimensional manifolds, Comm. Math. Phys. 272 (2007) 601 MR2304469
12 C J Earle, J Eells, The diffeomorphism group of a compact Riemann surface, Bull. Amer. Math. Soc. 73 (1967) 557 MR0212840
13 S Garoufalidis, J Levine, Finite type 3–manifold invariants, the mapping class group and blinks, J. Differential Geom. 47 (1997) 257 MR1601612
14 S M Gersten, A presentation for the special automorphism group of a free group, J. Pure Appl. Algebra 33 (1984) 269 MR761633
15 J Giansiracusa, U Tillmann, Vanishing of universal characteristic classes for handlebody groups and boundary bundles, J. Homotopy Relat. Struct. 6 (2011) 103 MR2818701
16 S Hirose, The action of the handlebody group on the first homology group of the surface, Kyungpook Math. J. 46 (2006) 399 MR2261393
17 D Johnson, An abelian quotient of the mapping class group g, Math. Ann. 249 (1980) 225 MR579103
18 D Johnson, Quadratic forms and the Birman–Craggs homomorphisms, Trans. Amer. Math. Soc. 261 (1980) 235 MR576873
19 D Johnson, The structure of the Torelli group I : A finite set of generators for , Ann. of Math. 118 (1983) 423 MR727699
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 D Johnson, The structure of the Torelli group III : The abelianization of g, Topology 24 (1985) 127 MR793179
22 M Korkmaz, A I Stipsicz, The second homology groups of mapping class groups of oriented surfaces, Math. Proc. Cambridge Philos. Soc. 134 (2003) 479 MR1981213
23 J Levine, Pure braids, a new subgroup of the mapping class group and finite-type invariants of 3–manifolds, from: "Tel Aviv Topology Conference : Rothenberg Festschrift (1998)" (editors M Farber, W Lück, S Weinberger), Contemp. Math. 231, Amer. Math. Soc. (1999) 137 MR1705580
24 J Levine, Homology cylinders: an enlargement of the mapping class group, Algebr. Geom. Topol. 1 (2001) 243 MR1823501
25 J Levine, The Lagrangian filtration of the mapping class group and finite-type invariants of homology spheres, Math. Proc. Cambridge Philos. Soc. 141 (2006) 303 MR2265877
26 J Milnor, Introduction to algebraic K–theory, 72, Princeton Univ. Press (1971) MR0349811
27 J Milnor, On the homology of Lie groups made discrete, Comment. Math. Helv. 58 (1983) 72 MR699007
28 S Morita, Characteristic classes of surface bundles, Invent. Math. 90 (1987) 551 MR914849
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 A Putman, The Picard group of the moduli space of curves with level structures arXiv:0908.0555
31 J Rosenberg, Algebraic K–theory and its applications, 147, Springer (1994) MR1282290
32 T Sakasai, The Johnson homomorphism and the third rational cohomology group of the Torelli group, Topology Appl. 148 (2005) 83 MR2118957
33 C Soulé, The cohomology of SL3(Z), Topology 17 (1978) 1 MR0470141
34 M R Stein, The Schur multipliers of Sp6(Z), Spin8(Z), Spin7(Z), and F4(Z), Math. Ann. 215 (1975) 165 MR0372056
35 W van der Kallen, The Schur multipliers of SL(3,Z) and SL(4,Z), Math. Ann. 212 (1974/75) 47 MR0354893