This is exercise 4.12 in The Knot Book. Show that the surface in the figure is compressible by finding a disk that intersects with the surface in the boundary which bounds no other disk in the surface.
2026-03-27 15:16:44.1774624604
How to show this surface is compressible
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In the part of the picture I have clipped below, if you squint, you can a sphere with four holes cut out, with two arcs connecting two pairs of holes. If you pinch off the holes then what you have is the first diagram on the bottom left.
Without going into too much detail, both transformations below can be reversed, along with the included pink disc, while retaining the property that the disc not intersect the strands. This will be your compression.