Quantum Topology / Hopf Algebra Seminar
Louis Kauffman
UIC
The Poincare Dodecahedral Space
Abstract: We will examine the Poincare Dodecahedral Space by representing it as the Brieskorn manifold
$\Sigma (2,3,5)$ and show that this manifold is the quotient of the action of binary dodecahedral group acting
on the three-dimensional sphere $S^{3}$ . This description shows that the Poincare Space is an $a$-fold branched covering
of $S^{3}$ along a $(b,c)$ torus knot where $\{a,b,c\} = \{2,3,5\}.$ We consider the question of a direct proof of this statement
from the definition of the Poincare Space as a dodecahedron with opposite face identifications.
Thursday March 9, 2017 at 2:00 PM in SEO 612