Volume 14 (2008)

Download this article
For screen
For printing
Recent Volumes
Volume 1, 1998
Volume 2, 1999
Volume 3, 2000
Volume 4, 2002
Volume 5, 2002
Volume 6, 2003
Volume 7, 2004
Volume 8, 2006
Volume 9, 2006
Volume 10, 2007
Volume 11, 2007
Volume 12, 2007
Volume 13, 2008
Volume 14, 2008
Volume 15, 2008
Volume 16, 2009
Volume 17, 2011
Volume 18, 2012
Volume 19, 2015
The Series
All Volumes
 
About this Series
Ethics Statement
Purchase Printed Copies
Author Index
ISSN 1464-8997 (online)
ISSN 1464-8989 (print)
 
MSP Books and Monographs
Other MSP Publications

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)