Reconstructing 4-manifolds from Morse 2-functions

Abstract

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.

13 pages, 10 figures. Replaced because the main theorem in the original is false. The theorem has been corrected and counterexamples to the original statement are given

References in corpus (1)

• Fiber connected, indefinite Morse 2-functions on connected n-manifolds