The Seifert genus is the smallest genus of a Seifert surface for the knot.
It minimizes the genus over all choices of Seifert surface.
The Seifert genus is additive under connected sum of knots:
(1)
The upper bound comes from boundary-connected-summing minimal Seifert surfaces, while the reverse inequality follows by cutting any Seifert surface for the connected sum along a splitting sphere.

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  1. Seifert surface
  2. Knot
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