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SUMMARY:Simple homotopy types of 4-manifolds (copy) - John Nicholson (Univ
 ersity of Glasgow)
DTSTART:20240529T091500Z
DTEND:20240529T100000Z
UID:TALK217441@talks.cam.ac.uk
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. The aim of this talk will be to present
  the first examples of two 4-manifolds which are homotopy equivalent but n
 ot simple homotopy equivalent\, as well as in all higher even dimensions. 
 The examples are constructed using surgery theory and the s-cobordism theo
 rem\, and are distinguished using methods from algebraic number theory and
  algebraic K-theory. This is joint work with Csaba Nagy and Mark Powell (a
 rXiv:2312.00322). I will also discuss progress on the question of whether 
 smooth 4-manifolds exist with these properties\, through joint work with D
 aniel Kasprowski and Simona Vesel&aacute\; (arXiv:2405.06637).
LOCATION:External
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