SIMPLY CONNECTED, SPINELESS 4-MANIFOLDS
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...
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| Veröffentlicht in: | Forum of mathematics. Sigma 2019, Vol.7, Article e14 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | 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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| ISSN: | 2050-5094 2050-5094 |
| DOI: | 10.1017/fms.2019.11 |