Hall 123

Knots and Links: 3- and 4-dimensional aspects

Swatee Naik

University of Nevada, Reno

Classical knot theory is the study of the placement of disjoint circles in
the three-dimensional space. Equivalence of two knots or links is via
homeomorphisms (bi-continuous deformations) of the three-space. A variety
of invariants arising from algebra, geometry and topology allow us to
distinguish between knots as well as study their properties. Moreover, any
three-dimensional manifold is obtained by surgery on a link; a process in
which we carve out disjoint knotted tori from the three-sphere and refill
them differently. Four dimensional manifolds are related through the
boundary three-manifolds and through knot concordance or cobordism.

In this talk we will introduce these notions and discuss some recent results
related to knots, links and 3- and 4-dimensional manifolds.