Reconstructing 4-manifolds from Morse 2-functions

Mathematics – Geometric Topology

Scientific paper

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13 pages, 10 figures. Replaced because the main theorem in the original is false. The theorem has been corrected and counterex

Scientific paper

Given a Morse 2-function $f: X^4 \to S^2$, we give minimal conditions on the
fold curves and fibers so that $X^4$ and $f$ can be reconstructed from a
certain combinatorial diagram attached to $S^2$. Additional remarks are made in
other dimensions.

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