My study has led me to (incompressible) branched surfaces as described in https://core.ac.uk/download/pdf/82332579.pdf

In the paper, the authors provide a great example, however I'm looking for more examples not in $S_{g}\times S^{1}$ to help my understanding.

Does anyone have any good (perhaps simple) examples? Maybe some examples of incompressible branched surfaces with boundary?

Thanks in advance!


Hatcher and Thurston give examples of branched surfaces with boundary in the exteriors of two-bridge knots. These branched surfaces are incompressible whenever each band contains at least two half-twists.


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