V. O. Manturov works on knot theory. With S. Kim (knot theory), he authored lectures connecting fundamental groups with diagrams of knots. The displayed title page verifies both sets of initials.[ref]
Lecture 3. Fundamental groups and knot groups by S. Kim and V. O. Manturov. Title page, 19 May 2022
Their presentation of knot groups explains how loops in a knot complement can be encoded by generators and relations. Wirtinger presentations use arcs, whereas a Dehn presentation of a knot group uses regions and crossing relations. The two constructions show how a picture supplies algebraic information about an otherwise difficult three-dimensional complement.[ref]
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