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arXiv:math.GT/9712255v21Mar1999 Annals of Mathematics, 149 (1999), 497510
 

Summary: arXiv:math.GT/9712255v21Mar1999
Annals of Mathematics, 149 (1999), 497­510
Scharlemann's manifold is standard
By Selman Akbulut*
Dedicated to Robion Kirby on the occasion of his 60th
birthday
Abstract
In his 1974 thesis, Martin Scharlemann constructed a fake homotopy
equivalence from a closed smooth manifold f : Q S3 × S1#S2 × S2, and
asked the question whether or not the manifold Q itself is diffeomorphic to
S3 × S1#S2 × S2. Here we answer this question affirmatively.
In [Sc] Scharlemann showed that if 3 is the Poincar´e homology 3-sphere,
by surgering the 4-manifold × S1
, along a loop in × 1 × S1
normally
generating the fundamental group of , one obtains a closed smooth manifold
Q and homotopy equivalence:
f : Q - S3
× S1
#S2

  

Source: Akbulut, Selman - Department of Mathematics, Michigan State University

 

Collections: Mathematics