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CATEGORIES:Differential Geometry and Topology Seminar
SUMMARY:Homological Stability of Moduli Spaces of High Dim
ensional Manifolds - Nina Friedrich\, Cambridge
DTSTART;TZID=Europe/London:20170517T160000
DTEND;TZID=Europe/London:20170517T170000
UID:TALK71673AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/71673
DESCRIPTION:Some sequences of topological spaces X1 --> X2 -->
X3 --> ... have the property\nthat the induced ma
ps in homology are eventually isomorphisms. There
are many examples\, where this phenomenon is alrea
dy known to hold. In this talk we will consider th
e example of diffeomorphism groups of high dimensi
onal manifolds. We first explain how to translate
homological stability in the geometric setting for
this example to the algebraic setting of quadrati
c forms. For simply-connected manifolds\, Galatius
and Randal-Williams have shown that certain simpl
icial complexes arising on the algebraic side are
highly connected\, and hence deduced homological s
tability theorems for moduli spaces of simply-conn
ected manifolds. We generalise this to a much larg
er class of manifolds (those having virtually poly
cyclic fundamental group).
LOCATION:MR13
CONTACT:Ivan Smith
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