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SIMPLY CONNECTED, SPINELESS 4-MANIFOLDS

Part of: Low-dimensional topology PL-topology

Published online by Cambridge University Press:  17 May 2019

ADAM SIMON LEVINE  and
TYE LIDMAN
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.

MSC classification

Primary: 57M27: Invariants of knots and 3-manifolds 57Q35: Embeddings and immersions
Type
Research Article
Information
Forum of Mathematics, Sigma , Volume 7 , 2019 , e14
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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