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CATEGORIES:Differential Geometry and Topology Seminar
SUMMARY:Simple homotopy types of even dimensional manifold
s - John Nicholson (Glasgow)
DTSTART;TZID=Europe/London:20240228T160000
DTEND;TZID=Europe/London:20240228T170000
UID:TALK209896AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/209896
DESCRIPTION:Two CW-complexes are said to be simple homotopy eq
uivalent if they are related by a sequence of coll
apses and expansions of cells. This notion interpo
lates between homeomorphism and homotopy in the se
nse that simple homotopy equivalent implies homoto
py equivalent\, and homeomorphic implies simple ho
motopy equivalent. It consequently proved extremel
y useful in manifold topology and is behind the s-
cobordism theorem which is the basis for the vast
majority of manifold classification results in dim
ension at least 4. The aim of this talk will be to
present the first examples of two 4-manifolds whi
ch are homotopy equivalent but not simple homotopy
equivalent\, as well as in all higher even dimens
ions. The examples are constructed using surgery t
heory and the s-cobordism theorem\, and are distin
guished using methods from algebraic number theory
and algebraic K-theory. I will also discuss a num
ber of new directions including progress on classi
fying the possible fundamental groups for which ex
amples exist. This is joint work with Csaba Nagy a
nd Mark Powell.
LOCATION:MR13
CONTACT:Oscar Randal-Williams
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