2019/11/17 by Skopenkov, A.
#57M27 #FOS: Mathematics #Geometric Topology (math.GT)
paper · doi:10.48550/arxiv.1911.07330
A 2018 paper by A. Levine and T. Lidman outlines a proof of the following interesting result in topology of manifolds: there is a compact smooth 4-manifold W with boundary such that W is homotopy equivalent to S2 but there does not exist an embedding S2→ W which is a homotopy equivalence and is simplicial for some triangulations of W and of S2. We present a shorter (and hopefully clearer) exposition. We reveal that some parts of the proof are missing, and that some results are used in that paper without proof or reference, or even without explicit statement.