Une construction intrinsèque du cœur de l'invariant de Casson
Pitsch, Wolfgang
Annales de l'Institut Fourier, Tome 51 (2001), p. 1741-1761 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU)

Nous donnons une nouvelle construction cohomologique du cœur de l'invariant de Casson et nous donnons un nouveau calcul de ses valeurs sur les générateurs du sous- groupe de Johnson du mapping class group.

We give a new cohomological construction of the core of Casson's invariant and give a new computation of its values on the generators of the Johnson subgroup of the mapping class group.

Publié le : 2001-01-01
DOI : https://doi.org/10.5802/aif.1873
Classification:  57M27,  20J05
Mots clés: invariant de Casson, groupe de Torelli, mapping class group 
@article{AIF_2001__51_6_1741_0,
     author = {Pitsch, Wolfgang},
     title = {Une construction intrins\`eque du c\oe ur de l'invariant de Casson},
     journal = {Annales de l'Institut Fourier},
     volume = {51},
     year = {2001},
     pages = {1741-1761},
     doi = {10.5802/aif.1873},
     zbl = {0983.57010},
     language = {fr},
     url = {http://dml.mathdoc.fr/item/AIF_2001__51_6_1741_0}
}

Pitsch, Wolfgang. Une construction intrinsèque du cœur de l'invariant de Casson. Annales de l'Institut Fourier, Tome 51 (2001) pp. 1741-1761. doi : 10.5802/aif.1873. http://gdmltest.u-ga.fr/item/AIF_2001__51_6_1741_0/

[Bro94] K.S. Brown Cohomology of Groups, Springer-Verlag, Graduate Texts in Mathematics, Tome 87 (1994) | MR 1324339 | Zbl 0584.20036

[Cerf61] J. Cerf Topologie de certains espaces de plongements, Gauthier-Villars, Bull. Soc. Math. France (1961) | Numdam | MR 140120 | Zbl 0101.16001

[Ea-Ee67] C.J. Earle; J. Eells The Diffeomorphism Group of a Compact Riemann Surface, Bull. Amer. Math. Soc., Tome 73 (1967), pp. 557-559 | Article | MR 212840 | Zbl 0196.09402

[Joh79] D. Johnson Homeomorphisms of a Surface which Act Trivially on Homology, Proc. Amer. Math. Soc., Tome 75 (1979), pp. 119-125 | Article | MR 529227 | Zbl 0407.57003

[Joh80a] D. Johnson An Abelian Quotient of the Mapping Class Group, Math. Ann., Tome 249 (1980), pp. 225-242 | Article | MR 579103 | Zbl 0409.57009

[Joh80b] D. Johnson Conjugacy Relations in Subgroups of the Mapping Class Group and a Group-Theoretic Description of the Rochlin Invariant, Math. Ann., Tome 249 (1980), pp. 243-263 | Article | MR 579104 | Zbl 0409.57010

[Joh85a] D. Johnson The Structure of the Torelli Group II : a Characterization of the Group Generated by Twists on Bounding Curves, Topology, Tome 24 (1985), pp. 113-126 | Article | MR 793178 | Zbl 0571.57009

[Joh85b] D. Johnson The Structure of the Torelli group III : the Abelianization of 𝒯, Topology, Tome 24 (1985), pp. 127-144 | MR 793179 | Zbl 0571.57010

[Lan66] S. Lang Rapport sur la cohomologie des groupes, W.A. Benjamin, Math. Lecture Note Series, Tome 4 (1966) | MR 212073 | Zbl 0171.28903

[Mey73] W. Meyer Die Signatur von Flächenbündeln, Math. Ann., Tome 201 (1973), pp. 239-264 | Article | MR 331382 | Zbl 0241.55019

[Mor89a] S. Morita Casson's Invariant for Homology 3-Spheres and Characteristic Classes of Surface Bundles I, Topology, Tome 28 (1989), pp. 305-323 | Article | MR 1014464 | Zbl 0684.57008

[Mor89b] S. Morita Families of Jacobian Manifolds and Characteristic Classes of Surface Bundles 1, Ann. Inst. Fourier, Tome 39 (1989) no. 3, pp. 777-810 | Article | Numdam | MR 1030850 | Zbl 0672.57015

[Nil27] J. Nielsen Untesuchungen zur Topologie der geschlossenen zweiseitigen Flächen I, Acta Math., Tome 50 (1927), pp. 189-358 | Article | JFM 53.0545.12

[Pit99a] W. Pitsch Un calcul élémentaire de H 2 (ℳ g,1 ,ℤ) pour g≥4, C.R.A.S., Sér. 1 Math., Tome 329 (1999) | MR 1724094

[Pit99b] W. Pitsch Extension verselles des groupes nilpotents libres (1999) (préprint Ecole Polytechnique)

[Rol90] D. Rolfsen Knots and Links, Publish or Perish, Inc., Math. Lecture Series, Tome 7 (1990) | MR 1277811 | Zbl 0854.57002

[Sma68] S. Smale Diffeomorphisms of the 2-Sphere, Proc. Math. Soc., Tome 10 (1959), pp. 621-626 | Article | MR 112149 | Zbl 0118.39103