Which fields are they? Maybe a ranking if you can give one.
The simplest field I can think of consists of one number 0. The next simplest consists of two numbers (0 and 1) using modulo 2 for addition. After this things get more complicated.
I had thought the question was about fields of work or professions! Veterinary medicine came to mind.
fields (non mathematical term) in maths.
As far as I know, Sally Field has a very minimal amount of geometry/topology in her work. I think there was a scene of her doing some algebra in an episode of Gidget.
A little bit more seriously, "Abstract Algebra" as a general field is usually distinguished form Topology/geometry. Other forms of mathematics typically include some algebra and some topology.
But still it's very related in a way since one can define geometry in terms of algebraic concepts. What is something that is so far from topology and geometry that there is not the slightest connection?
It is very hard to find a branch of mathematics that has absolutely no connection to geometry or topology, particularly since you don't think abstract algebra is not far enough away. I could suggest number theory but then the pythagorean theorem might turn you off. Also abstract probability theory could qualify, as long as you don't use Borel fields for sigma fields.
So maybe analysis related stuff? How about mathematical logic?
Separate names with a comma.