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  1. ; ; ; ; (, Bulletin of the London Mathematical Society)
  2. ; (, Bulletin of the London Mathematical Society)
  3. ; (, Forum of Mathematics, Sigma)
    We construct infinitely many compact, smooth 4-manifolds which are homotopy equivalent to $$S^{2}$$ but do not admit a spine (that is, a piecewise linear embedding of $$S^{2}$$ that realizes the homotopy equivalence). This is the remaining case in the existence problem for codimension-2 spines in simply connected manifolds. The obstruction comes from the Heegaard Floer $$d$$ invariants. 
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