A standard form of incompressible surfaces in 3-dimensional handlebodies

Wei Lin; Fengchun Lei

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arXiv · 2212.05769

A standard form of incompressible surfaces in 3-dimensional handlebodies

Wei Lin·Fengchun Lei

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Abstract

Applying Morse theory, we give a standard form for a class of surfaces which includes all the properly embedded incompressible surfaces in 3-dimensional handlebodies. We also give a necessary and sufficient condition to determine the incompressibility of such surfaces placed in our standard form. Our algorithm is practical. Several examples are given to test the algorithm.

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Wei Lin, Fengchun Lei. 2022-12-12. A standard form of incompressible surfaces in 3-dimensional handlebodies. https://arxiv.org/abs/2212.05769

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