Simply-connected, spineless 4-manifolds

2018/03/05 by Levine, Adam Simon, Lidman, Tye
#57M27 #57Q35 #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.1803.01765

Abstract

We construct infinitely many smooth 4-manifolds which are homotopy equivalent to S² but do not admit a spine, i.e., a piecewise-linear embedding of S² which 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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