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arXiv:2212.05769 [math.GT]AbstractReferencesReviewsResources

A standard form of incompressible surfaces in 3-dimensional handlebodies

Wei Lin, Fengchun Lei

Published 2022-12-12Version 1

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.

Comments: 19 pages, 13 figures. Accepted for publication in SCIENCE CHINA Mathematics
Categories: math.GT
Subjects: 57K30, 57N75, 57R65
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