#### Volume 12, issue 1 (2012)

 Download this article For screen For printing
 Recent Issues
 The Journal About the Journal Editorial Board Editorial Interests Author Index Editorial procedure Submission Guidelines Submission Page Author copyright form Subscriptions Contacts G&T Publications GTP Author Index ISSN (electronic): 1472-2739 ISSN (print): 1472-2747

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) 2117–2161 MR2680201 2 V I Arnol'd, The cohomology ring of the group of dyed braids, Mat. Zametki 5 (1969) 227–231 MR0242196 3 J S Birman, Braids, links, and mapping class groups, Ann. of Math. Studies 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) 137–164 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) 119–134 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) 283–309 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) 21–55 MR642850 8 N Broaddus, B Farb, A Putman, Irreducible Sp–representations and subgroup distortion in the mapping class group, Comment. Math. Helv. 86 (2011) 537–556 MR2803852 9 K S Brown, Cohomology of groups, Graduate Texts in Math. 87, Springer (1982) MR672956 10 D Cheptea, K Habiro, G Massuyeau, A functorial LMO invariant for Lagrangian cobordisms, Geom. Topol. 12 (2008) 1091–1170 MR2403806 11 D Cheptea, T T Q Le, A TQFT associated to the LMO invariant of three-dimensional manifolds, Comm. Math. Phys. 272 (2007) 601–634 MR2304469 12 C J Earle, J Eells, The diffeomorphism group of a compact Riemann surface, Bull. Amer. Math. Soc. 73 (1967) 557–559 MR0212840 13 S Garoufalidis, J Levine, Finite type 3–manifold invariants, the mapping class group and blinks, J. Differential Geom. 47 (1997) 257–320 MR1601612 14 S M Gersten, A presentation for the special automorphism group of a free group, J. Pure Appl. Algebra 33 (1984) 269–279 MR761633 15 J Giansiracusa, U Tillmann, Vanishing of universal characteristic classes for handlebody groups and boundary bundles, J. Homotopy Relat. Struct. 6 (2011) 103–112 MR2818701 16 S Hirose, The action of the handlebody group on the first homology group of the surface, Kyungpook Math. J. 46 (2006) 399–408 MR2261393 17 D Johnson, An abelian quotient of the mapping class group Ig, Math. Ann. 249 (1980) 225–242 MR579103 18 D Johnson, Quadratic forms and the Birman–Craggs homomorphisms, Trans. Amer. Math. Soc. 261 (1980) 235–254 MR576873 19 D Johnson, The structure of the Torelli group I: A finite set of generators for \cal I, Ann. of Math. 118 (1983) 423–442 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) 113–126 MR793178 21 D Johnson, The structure of the Torelli group III: The abelianization of Ig, Topology 24 (1985) 127–144 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) 479–489 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) 137–157 MR1705580 24 J Levine, Homology cylinders: an enlargement of the mapping class group, Algebr. Geom. Topol. 1 (2001) 243–270 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) 303–315 MR2265877 26 J Milnor, Introduction to algebraic K–theory, Ann. of Math. Studies 72, Princeton Univ. Press (1971) MR0349811 27 J Milnor, On the homology of Lie groups made discrete, Comment. Math. Helv. 58 (1983) 72–85 MR699007 28 S Morita, Characteristic classes of surface bundles, Invent. Math. 90 (1987) 551–577 MR914849 29 S Morita, The extension of Johnson's homomorphism from the Torelli group to the mapping class group, Invent. Math. 111 (1993) 197–224 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, Graduate Texts in Math. 147, Springer (1994) MR1282290 32 T Sakasai, The Johnson homomorphism and the third rational cohomology group of the Torelli group, Topology Appl. 148 (2005) 83–111 MR2118957 33 C Soulé, The cohomology of SL3(Z), Topology 17 (1978) 1–22 MR0470141 34 M R Stein, The Schur multipliers of Sp6(Z), Spin8(Z), Spin7(Z), and F4(Z), Math. Ann. 215 (1975) 165–172 MR0372056 35 W van der Kallen, The Schur multipliers of SL(3,Z) and SL(4,Z), Math. Ann. 212 (1974/75) 47–49 MR0354893