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Homological Stability of Moduli Spaces of High Dimensional Manifolds
If you have a question about this talk, please contact Ivan Smith.
Some sequences of topological spaces X1 —> X2 —> X3 —> ... have the property that the induced maps in homology are eventually isomorphisms. There are many examples, where this phenomenon is already known to hold. In this talk we will consider the example of diffeomorphism groups of high dimensional manifolds. We first explain how to translate homological stability in the geometric setting for this example to the algebraic setting of quadratic forms. For simply-connected manifolds, Galatius and Randal-Williams have shown that certain simplicial complexes arising on the algebraic side are highly connected, and hence deduced homological stability theorems for moduli spaces of simply-connected manifolds. We generalise this to a much larger class of manifolds (those having virtually polycyclic fundamental group).
This talk is part of the Differential Geometry and Topology Seminar series.
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