Quandles and codimension two embeddings

Abstract: Distributivity has been an integral part of logic for a long time. An attempt to decouple them in linear logic applied to quantum mechanics was not successful. Distributivity in topology is a more recent development and can be dated to the PhD dissertation of Joyce in 1979, in which quandles were applied to knot theory. The next push came with construction of homology theory for quandles by Fenn, Rourke, and Sanderson (between 1990 and 1995). In 1998, Carter, Kamada, and Saito
discovered how to use homology of quandles to study classical and higher-dimensional knots. From that time we observe an exponential growth of the topic, and it is my pleasure to report that it was achieved partly by work of our students. In this I talk will offer a gentle introduction to this unusually successful use of distributivity in
knot theory.