S. Kim (knot theory) coauthored lectures on fundamental groups and knot groups with V. O. Manturov. The primary title page identifies the author only as S. Kim; a fuller personal identity is not inferred from those initials.[ref]
Lecture 3. Fundamental groups and knot groups by S. Kim and V. O. Manturov. Title page, 19 May 2022
The lectures explain the van Kampen theorem and derive diagrammatic group presentations. A Dehn presentation of a knot group assigns generators to regions and a relation at each crossing, converting topological gluing into algebra. This supplies a reusable route from knot diagrams to invariants of their complements.[ref]
Lecture 3. Fundamental groups and knot groups by S. Kim and V. O. Manturov. Slides 12–21, especially the region/crossing figure
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