The Kazhdan property of the mapping class group of closed surfaces and the first cohomology group of its cofinite subgroups
Taherkhani, Feraydoun
Experiment. Math., Tome 9 (2000) no. 3, p. 261-274 / Harvested from Project Euclid
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We show that the mapping class group of a closed surface of genus 2 does not satisfy the Kazhdan property by constructing subgroups of finite index having a nonvanishing first cohomology group. We also construct some subgroups of finite index in the mapping class group of a genus 3 surface and calculate their first cohomology groups, which all turn out to be trivial. Most of the calculations have been carried out by computer using GAP.
Publié le : 2000-05-14
Classification:  57M07,  20F38 
@article{1045952350,
     author = {Taherkhani, Feraydoun},
     title = {The Kazhdan property of the mapping class group of closed surfaces and the first cohomology group of its cofinite subgroups},
     journal = {Experiment. Math.},
     volume = {9},
     number = {3},
     year = {2000},
     pages = { 261-274},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1045952350}
}

Taherkhani, Feraydoun. The Kazhdan property of the mapping class group of closed surfaces and the first cohomology group of its cofinite subgroups. Experiment. Math., Tome 9 (2000) no. 3, pp.  261-274. http://gdmltest.u-ga.fr/item/1045952350/