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!



Example incompressible branched surfaces
[Hatcher and Thurston](https://link.springer.com/article/10.1007/BF01388971) 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.


