I know that every compact 2D surface can be thought of as a sphere with a certain number of handles and Möbius strips attached. Given a knot diagram, is it trivial to understand what 2D surface one obtains by replacing the "wire" (BTW, what's the math jargon for the lace?) with a tube? My guess is that we shall always obtain different embedings of a usual torus into 3D. If so, are there more interesting ways to obtain 2D surfaces from knots by more interesting mappings?
2026-03-25 16:20:39.1774455639
Knots into 2D surfaces
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