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SUMMARY:Simple homotopy types of even dimensional manifolds - John Nichols
 on (Glasgow)
DTSTART:20240228T160000Z
DTEND:20240228T170000Z
UID:TALK209896@talks.cam.ac.uk
CONTACT:Oscar Randal-Williams
DESCRIPTION:Two CW-complexes are said to be simple homotopy equivalent if 
 they are related by a sequence of collapses and expansions of cells. This 
 notion interpolates between homeomorphism and homotopy in the sense that s
 imple homotopy equivalent implies homotopy equivalent\, and homeomorphic i
 mplies simple homotopy equivalent. It consequently proved extremely useful
  in manifold topology and is behind the s-cobordism theorem which is the b
 asis for the vast majority of manifold classification results in dimension
  at least 4. The aim of this talk will be to present the first examples of
  two 4-manifolds which are homotopy equivalent but not simple homotopy equ
 ivalent\, as well as in all higher even dimensions. The examples are const
 ructed using surgery theory and the s-cobordism theorem\, and are distingu
 ished using methods from algebraic number theory and algebraic K-theory. I
  will also discuss a number of new directions including progress on classi
 fying the possible fundamental groups for which examples exist. This is jo
 int work with Csaba Nagy and Mark Powell.
LOCATION:MR13
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