= V. O. Manturov
{c}
<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.<Lecture 3. Fundamental groups and knot groups by S. Kim and V. O. Manturov>[Title page, 19 May 2022]{ref}
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.<Lecture 3. Fundamental groups and knot groups by S. Kim and V. O. Manturov>[Slides 12–21]{ref}
Back to article page
