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SIMPLY CONNECTED, SPINELESS 4-MANIFOLDS

Published online by Cambridge University Press:  17 May 2019

ADAM SIMON LEVINE
Affiliation:
Department of Mathematics, Duke University, Durham, NC 27708, USA; [email protected]
TYE LIDMAN
Affiliation:
Department of Mathematics, North Carolina State University, Raleigh, NC 27607, USA; [email protected]

Abstract

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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.

Type
Research Article
Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© The Author(s) 2019

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