Geodesic
Homological Stability of Automorphism Groups of Quadratic Modules and Manifolds
Documenta mathematica, Tome 22 (2017), pp. 1729-1774
Cet article a éte moissonné depuis la source EMS Press

Voir la notice de l'article

We prove homological stability for both general linear groups of modules over a ring with finite stable rank and unitary groups of quadratic modules over a ring with finite unitary stable rank. In particular, we do not assume the modules and quadratic modules to be well-behaved in any sense: for example, the quadratic form may be singular. This extends results by van der Kallen and Mirzaii-van der Kallen respectively. Combining these results with the machinery introduced by Galatius-Randal-Williams to prove homological stability for moduli spaces of simply-connected manifolds of dimension 2n≥6, we get an extension of their result to the case of virtually polycyclic fundamental groups.
DOI : 10.4171/dm/609
Classification : 19B10, 19B14, 19G05, 57S05 
@article{10_4171_dm_609,
     author = {Nina Friedrich},
     title = {Homological {Stability} of {Automorphism} {Groups} of {Quadratic} {Modules} and {Manifolds}},
     journal = {Documenta mathematica},
     pages = {1729--1774},
     year = {2017},
     volume = {22},
     doi = {10.4171/dm/609},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/609/}
}
TY  - JOUR
AU  - Nina Friedrich
TI  - Homological Stability of Automorphism Groups of Quadratic Modules and Manifolds
JO  - Documenta mathematica
PY  - 2017
SP  - 1729
EP  - 1774
VL  - 22
UR  - http://geodesic.mathdoc.fr/articles/10.4171/dm/609/
DO  - 10.4171/dm/609
ID  - 10_4171_dm_609
ER  - 
%0 Journal Article
%A Nina Friedrich
%T Homological Stability of Automorphism Groups of Quadratic Modules and Manifolds
%J Documenta mathematica
%D 2017
%P 1729-1774
%V 22
%U http://geodesic.mathdoc.fr/articles/10.4171/dm/609/
%R 10.4171/dm/609
%F 10_4171_dm_609
Nina Friedrich. Homological Stability of Automorphism Groups of Quadratic Modules and Manifolds. Documenta mathematica, Tome 22 (2017), pp. 1729-1774. doi: 10.4171/dm/609

Cité par Sources :