Geodesic
Partial Torelli groups and homological stability
Putman, Andrew1
1 Department of Mathematics, University of Notre Dame, Notre Dame, IN, United States
Algebraic and Geometric Topology, Tome 23 (2023) no. 8, pp. 3417-3496

Voir la notice de l'article provenant de la source Mathematical Sciences Publishers

We prove a homological stability theorem for the subgroup of the mapping class group acting as the identity on some fixed portion of the first homology group of the surface. We also prove a similar theorem for the subgroup of the mapping class group preserving a fixed map from the fundamental group to a finite group, which can be viewed as a mapping class group version of a theorem of Ellenberg, Venkatesh and Westerland about braid groups. These results require studying various simplicial complexes formed by subsurfaces of the surface, generalizing work of Hatcher and Vogtmann.

DOI : 10.2140/agt.2023.23.3417
Keywords: mapping class group, Torelli group, homological stability

Putman, Andrew 1

1 Department of Mathematics, University of Notre Dame, Notre Dame, IN, United States 
@article{10_2140_agt_2023_23_3417,
     author = {Putman, Andrew},
     title = {Partial {Torelli} groups and homological stability},
     journal = {Algebraic and Geometric Topology},
     pages = {3417--3496},
     publisher = {mathdoc},
     volume = {23},
     number = {8},
     year = {2023},
     doi = {10.2140/agt.2023.23.3417},
     url = {http://geodesic.mathdoc.fr/articles/10.2140/agt.2023.23.3417/}
}
TY  - JOUR
AU  - Putman, Andrew
TI  - Partial Torelli groups and homological stability
JO  - Algebraic and Geometric Topology
PY  - 2023
SP  - 3417
EP  - 3496
VL  - 23
IS  - 8
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.2140/agt.2023.23.3417/
DO  - 10.2140/agt.2023.23.3417
ID  - 10_2140_agt_2023_23_3417
ER  - 
%0 Journal Article
%A Putman, Andrew
%T Partial Torelli groups and homological stability
%J Algebraic and Geometric Topology
%D 2023
%P 3417-3496
%V 23
%N 8
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.2140/agt.2023.23.3417/
%R 10.2140/agt.2023.23.3417
%F 10_2140_agt_2023_23_3417
Putman, Andrew. Partial Torelli groups and homological stability. Algebraic and Geometric Topology, Tome 23 (2023) no. 8, pp. 3417-3496. doi: 10.2140/agt.2023.23.3417

Cité par Sources :