In this course Weise stated several famous open problems in topology, including the Poincare Conjecture, the Four Colour Problem and the Unknot Problem. This experience marked the …

Haken, H. [Atom- und Quantenphysik. English] The physics of atoms and quanta: introduction to experiments and theory / H. Haken, H. C. Wolf; translated by W. D. Brewer. - 3rd corrected …

The structure of a hierarchy opens the possibility of inductive proofs of theorems about Haken 3-manifolds; Thurston’s famous geometrization theorem for Haken 3-manifolds is such an example.

This provides an algorithm for deciding if a knot is the unknot by applying Haken’s theory to the complement of the knot. Haken’s paper was 130 pages long and his algorithm has never been …

Wolfgang Haken (1928-–2022) was a German American math-ematician who made pathbreaking contributions to topology and graph theory, most notably the discovery of an algorithm to …

Roughly speaking, a Haken n-manifold is an n-manifold that can be cut open successively along “essential” codimension-one submanifolds, until one obtains a finite collection of n-cells. A few …

Theorem 1.1 (Haken, Casson–Gordon) There is a @–reducing disk E for M such that @E D @D, E intersects T in a single essential circle (ie E @–reduces T ). Note that D and E are isotopic if …