Reconstructing 4-manifolds from Morse 2-functions

David T. Gay; Robion Kirby

doi:10.2140/gtm.2012.18.103

Reconstructing 4-manifolds from Morse 2-functions

Geometric Topology 2016-01-20 v2

Authors: David T. Gay , Robion Kirby

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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.

Keywords

smooth 4-manifolds morse theory

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@article{arxiv.1202.3487,
  title  = {Reconstructing 4-manifolds from Morse 2-functions},
  author = {David T. Gay and Robion Kirby},
  journal= {arXiv preprint arXiv:1202.3487},
  year   = {2016}
}

Comments

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

Reconstructing 4-manifolds from Morse 2-functions

Abstract

Keywords

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