Geodesic
SIMPLY CONNECTED, SPINELESS 4-MANIFOLDS
Forum of Mathematics, Sigma, Tome 7 (2019)

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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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     author = {ADAM SIMON LEVINE and TYE LIDMAN},
     title = {SIMPLY {CONNECTED,} {SPINELESS} {4-MANIFOLDS}},
     journal = {Forum of Mathematics, Sigma},
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     doi = {10.1017/fms.2019.11},
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     url = {http://geodesic.mathdoc.fr/articles/10.1017/fms.2019.11/}
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ADAM SIMON LEVINE; TYE LIDMAN. SIMPLY CONNECTED, SPINELESS 4-MANIFOLDS. Forum of Mathematics, Sigma, Tome 7 (2019). doi: 10.1017/fms.2019.11

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