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Showing 1 to 3 of 3 for “"Homological Stability"”.
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Homological stability of spaces of manifolds via E_k-algebras
In this thesis we study homological stability properties of different families of spaces using the technique of cellular *E<sub>k</sub>*-algebras. Firstly, we will consider spin mapping class groups of surfaces, and their algebraic analogue —quadratic symplectic groups— using cellular …
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Linking Forms, Singularities, and Homological Stability for Diffeomorphism Groups of Odd Dimensional Manifolds
Let n > 1. We prove a homological stability theorem for the diffeomorphism groups of (4n+1)-dimensional manifolds, with respect to forming the connected sum with (2n-1)-connected, (4n+1)-dimensional manifolds that are stably parallelizable. Our techniques involve the study of the action of the …
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Automorphism Groups of Quadratic Modules and Manifolds
In this thesis 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 …