Topological classification of genus 1 Morse functions on S^3
DOI:
https://doi.org/10.15673/2072-9812.4/2014.41443Keywords:
Morse functions, topological classification, 3-sphereAbstract
We study the question about a topological classification of Morse functions on the 3-sphere, all critical points of which lie on a different level surfaces. The classification provides with respect to the group Diff0(S3) x Diff0(R) - the group of orientation-preserving diffeomorphisms of the source and the target. We give a description of a corresponding oriented graphs (Kronrod-Reeb graphs). It is shown that these graphs completely classify genus 1 functions. These functions has a property that the genus of all the components of their level surfaces is not greater then 1. Moreover, all these graphs can be realized by a genus 1 functions, thus they can not distinguish a topological type of a more complex functions.References
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