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Homology of the mapping class group Γ2,1 for surfaces of genus 2 with a boundary curve

Jochen Abhau, Carl-Friedrich Bödigheimer and Ralf Ehrenfried

Geometry & Topology Monographs 14 (2008) 1–25

DOI: 10.2140/gtm.2008.14.1

Bibliography
1 J Abhau, Die Homologie von Modulräumen Riemannscher Flächen – Berechnungen für g\leq2, Diplom thesis, Universität Bonn (2005)
2 V I Arnol'd, The cohomology ring of the group of dyed braids, Mat. Zametki 5 (1969) 227–231 MR0242196
3 V I Arnol'd, Certain topological invariants of algebrac functions, Trudy Moskov. Mat. Obšč. 21 (1970) 27–46 MR0274462
4 D J Benson, F R Cohen, Mapping class groups of low genus and their cohomology, Mem. Amer. Math. Soc. 90 (1991) MR1052554
5 C F Bödigheimer, The Hilbert uniformization I, in preparation
6 C F Bödigheimer, The topology of moduli spaces, part I: Hilbert uniformization, Math. Gott. Preprint Series SFB 170 9 (1990)
7 C F Bödigheimer, Configuration models for moduli spaces of Riemann surfaces with boundary, Abh. Math. Sem. Univ. Hamburg 76 (2006) 191–233 MR2293442
8 C F Bödigheimer, F R Cohen, M D Peim, Mapping class groups and function spaces, from: "Homotopy methods in algebraic topology (Boulder, CO, 1999)", Contemp. Math. 271, Amer. Math. Soc. (2001) 17–39 MR1831345
9 F Cohen, Cohomology of braid spaces, Bull. Amer. Math. Soc. 79 (1973) 763–766 MR0321074
10 F Cohen, The homology of Cn+1-spaces, n ≥ 0, from: "The Homology of Iterated Loop Spaces" (editors F R Cohen, T J Lada, J P May), Lecture Notes in Mathematics 533, Springer (1976) 207–353
11 J Ebert, The Hilbert uniformization II, in preparation
12 J Ebert, Über den Modulraum mehrfach gerichteter und punktierter Kleinscher Flächen, Diplom thesis, Universität Bonn (2003)
13 R Ehrenfried, Die Homologie der Modulräume berandeter Riemannscher Flächen von kleinem Geschlecht, Bonner Mathematische Schriften 306, Universität Bonn Mathematisches Institut (1998) MR1938981 PhD thesis, Universität Bonn (1997)
14 D B Fuks, Cohomology of the braid group mod 2, Funkcional. Anal. i Priložen. 4 (1970) 62–73 MR0274463
15 S Galatius, Mod p homology of the stable mapping class group, Topology 43 (2004) 1105–1132 MR2079997
16 H Glover, G Mislin, Torsion in the mapping class group and its cohomology, from: "Proceedings of the Northwestern conference on cohomology of groups (Evanston, Ill., 1985)" (1987) 177–189 MR885103
17 V Godin, The unstable integral homology of the mapping class groups of a surface with boundary, Math. Ann. 337 (2007) 15–60 MR2262776
18 J Harer, The second homology group of the mapping class group of an orientable surface, Invent. Math. 72 (1983) 221–239 MR700769
19 J L Harer, Stability of the homology of the mapping class groups of orientable surfaces, Ann. of Math. (2) 121 (1985) 215–249 MR786348
20 J L Harer, The virtual cohomological dimension of the mapping class group of an orientable surface, Invent. Math. 84 (1986) 157–176 MR830043
21 J L Harer, The cohomology of the moduli space of curves, from: "Theory of moduli (Montecatini Terme, 1985)", Lecture Notes in Math. 1337, Springer (1988) 138–221 MR963064
22 J Harer, The third homology group of the moduli space of curves, Duke Math. J. 63 (1991) 25–55 MR1106936
23 N V Ivanov, Mapping class groups, from: "Handbook of geometric topology", North-Holland (2002) 523–633 MR1886678
24 M Korkmaz, First homology group of mapping class groups of nonorientable surfaces, Math. Proc. Cambridge Philos. Soc. 123 (1998) 487–499 MR1607985
25 M Korkmaz, Low-dimensional homology groups of mapping class groups: a survey, Turkish J. Math. 26 (2002) 101–114 MR1892804
26 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
27 E Looijenga, Cohomology of M3 and M¹3, from: "Mapping class groups and moduli spaces of Riemann surfaces (Göttingen, 1991/Seattle, WA, 1991)", Contemp. Math. 150, Amer. Math. Soc. (1993) 205–228 MR1234266
28 I Madsen, M Weiss, The stable moduli space of Riemann surfaces: Mumford's conjecture, arXiv:math.AT/0212321
29 S Morita, Families of Jacobian manifolds and characteristic classes of surface bundles I, Ann. Inst. Fourier (Grenoble) 39 (1989) 777–810 MR1030850
30 M Müller, Orientierbarkeit des Raumes der Parallelschlitzgebiete, Diplom thesis, Universität Bonn (1996)
31 D Mumford, Abelian quotients of the Teichmüller modular group, J. Analyse Math. 18 (1967) 227–244 MR0219543
32 W Pitsch, Un calcul élémentaire de H2(Mg,1,Z) pour g\geq4, C. R. Acad. Sci. Paris Sér. I Math. 329 (1999) 667–670 MR1724094
33 J Powell, Two theorems on the mapping class group of a surface, Proc. Amer. Math. Soc. 68 (1978) 347–350 MR0494115
34 S Schardt, Die Hopf-Struktur auf der Konjugation-Shuffle-Algebra der symmetrischen Gruppen, Diplom thesis, Universität Bonn (2003)
35 O Tommasi, Rational cohomology of the moduli space of genus 4 curves, Compos. Math. 141 (2005) 359–384 MR2134272
36 O Tommasi, Rational cohomology of M3,2, Compos. Math. 143 (2007) 986–1002 MR2339836
37 F V Vaĭnšteĭn, The cohomology of braid groups, Funktsional. Anal. i Prilozhen. 12 (1978) 72–73 MR498903
38 M Zaw, The moduli space of non-classical directed Klein surfaces, Bonner Mathematische Schriften 313, Universität Bonn Mathematisches Institut (1998) MR1933809 PhD thesis, Universität Bonn (1998)