Geodesic
Homological Stability of Automorphism Groups of Quadratic Modules and Manifolds
Documenta mathematica, Tome 22 (2017), pp. 1729-1774

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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 
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
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     title = {Homological {Stability} of {Automorphism} {Groups} of {Quadratic} {Modules} and {Manifolds}},
     journal = {Documenta mathematica},
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