Quantum Topology / Hopf Algebra Seminar
Louis Kauffman
UIC
Knots, Brieskorn Manifolds and Branched Coverings
Abstract: This is an introductory talk about the remarkable properties of the algebraic varieties associated with the
complex polynomials $ z_{1}^{a_1} + \cdots z_{n}^{a_n}$ and the links of their singularities. The link of a singularity
is the intersection of a small sphere, centered at the singularity, with the algebraic variety. The link of singularity
at the origin of the above variety is denoted $\Sigma(a_1,\cdots,a_n)$ and is called the Brieskorn Manifold of that
type. Torus knots and links occur as $\Sigma(a,b).$ The Poincare manifold is $\Sigma(2,3,5).$ Higher dimensions
yield exotic spheres such as the family of Milnor spheres $\Sigma(6k-1,3,2,2,2).$ A good reference for this talk
is the book by John Milnor, "Singularities of Complex Hypersurfaces."
Thursday February 23, 2017 at 2:00 PM in SEO 612