The slice genus is a concept from the field of topology, specifically in the study of 4-manifolds and knot theory. It is defined as follows: 1. **Knot Theory Context**: In knot theory, the slice genus of a knot in 3-dimensional space is a measure of how "simple" the knot is in terms of being able to be represented as the boundary of a smooth, oriented surface in a 4-dimensional space.
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The slice genus is the smallest genus of a smooth compact connected oriented surface properly embedded in with boundary .