Geodesic
Arithmetic group symmetry and finiteness properties of Torelli groups
Alexandru Dimca1 ; Stefan Papadima2
1 Institut Universitaire de France et Laboratoire J.A. Dieudonné, Université de Nice Sophia-Antipolis, Nice, France
2 Simion Stoilow Institute of Mathematics, Bucharest, Romania
Annals of mathematics, Tome 177 (2013) no. 2, pp. 395-423.

Voir la notice de l'article provenant de la source Annals of Mathematics website

We examine groups whose resonance varieties, characteristic varieties and Sigma-invariants have a natural arithmetic group symmetry, and we explore implications on various finiteness properties of subgroups. We compute resonance varieties, characteristic varieties and Alexander polynomials of Torelli groups, and we show that all subgroups containing the Johnson kernel have finite first Betti number, when the genus is at least $4$. We also prove that, in this range, the $I$-adic completion of the Alexander invariant is finite-dimensional, and the Kahler property for the Torelli group implies the finite generation of the Johnson kernel.
DOI : 10.4007/annals.2013.177.2.1

Alexandru Dimca 1 ; Stefan Papadima 2

1 Institut Universitaire de France et Laboratoire J.A. Dieudonné, Université de Nice Sophia-Antipolis, Nice, France
2 Simion Stoilow Institute of Mathematics, Bucharest, Romania 
@article{10_4007_annals_2013_177_2_1,
     author = {Alexandru Dimca and Stefan Papadima},
     title = {Arithmetic group symmetry and finiteness properties of {Torelli} groups},
     journal = {Annals of mathematics},
     pages = {395--423},
     publisher = {mathdoc},
     volume = {177},
     number = {2},
     year = {2013},
     doi = {10.4007/annals.2013.177.2.1},
     mrnumber = {3010803},
     zbl = {06156612},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4007/annals.2013.177.2.1/}
}
TY  - JOUR
AU  - Alexandru Dimca
AU  - Stefan Papadima
TI  - Arithmetic group symmetry and finiteness properties of Torelli groups
JO  - Annals of mathematics
PY  - 2013
SP  - 395
EP  - 423
VL  - 177
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4007/annals.2013.177.2.1/
DO  - 10.4007/annals.2013.177.2.1
LA  - en
ID  - 10_4007_annals_2013_177_2_1
ER  - 
%0 Journal Article
%A Alexandru Dimca
%A Stefan Papadima
%T Arithmetic group symmetry and finiteness properties of Torelli groups
%J Annals of mathematics
%D 2013
%P 395-423
%V 177
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4007/annals.2013.177.2.1/
%R 10.4007/annals.2013.177.2.1
%G en
%F 10_4007_annals_2013_177_2_1
Alexandru Dimca; Stefan Papadima. Arithmetic group symmetry and finiteness properties of Torelli groups. Annals of mathematics, Tome 177 (2013) no. 2, pp. 395-423. doi : 10.4007/annals.2013.177.2.1. http://geodesic.mathdoc.fr/articles/10.4007/annals.2013.177.2.1/

Cité par Sources :