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SUMMARY:Homological Stability of Moduli Spaces of High Dimensional Manifol
 ds - Nina Friedrich\, Cambridge
DTSTART:20170517T150000Z
DTEND:20170517T160000Z
UID:TALK71673@talks.cam.ac.uk
CONTACT:Ivan Smith
DESCRIPTION:Some sequences of topological spaces X1 --> X2 --> X3 --> ... 
 have the property\nthat the induced maps in homology are eventually isomor
 phisms. There are many examples\, where this phenomenon is already known t
 o hold. In this talk we will consider the example of diffeomorphism groups
  of high dimensional manifolds. We first explain how to translate homologi
 cal stability in the geometric setting for this example to the algebraic s
 etting of quadratic forms. For simply-connected manifolds\, Galatius and R
 andal-Williams have shown that certain simplicial complexes arising on the
  algebraic side are highly connected\, and hence deduced homological stabi
 lity theorems for moduli spaces of simply-connected manifolds. We generali
 se this to a much larger class of manifolds (those having virtually polycy
 clic fundamental group).
LOCATION:MR13
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