While reading this question posted at this link:
i interestingly landed up on this Wikipedia page, and was quite amazed to see the variety of branches opening up. That's how I came to know about the subject Arithmetic Topology. Wikipedia describes this subject as:
- Arithmetic topology is an area of mathematics that is a combination of algebraic number theory and topology. In the 1960s topological interpretations of class field theory were given by John Tate based on Galois cohomology, and also by Michael Artin and Jean-Louis Verdier based on Étale cohomology. In subsequent years, Barry Mazur and Yuri Manin pointed out a series of analogies between prime ideals and knots.
Can anyone explain me as to how Prime Ideals and Knot's are analogous (elementary explanation would be helpful) and why are we interested in studying these analogies.