I am currently in the process of turning my math doctoral thesis into articles to submit to journals. This is my first time writing anything mathematical for publication.
My thesis was on the long-side, and referenced a lot of background material from areas of math that do not often communicate. (The principle field is topology, but it draws heavily on some specific corners of algebra, number theory and relativity theory that most topologists do not study.) It also has a historical component and the first result is a completion of a somewhat archaic classical idea. I then go on to develop that idea to obtain results pertinent to current active research.
Due to this, as well as the common advice of not making an article too long (especially one’s first article), I am breaking my results into two articles. The first one will say something about what I intend to do in the second for motivational purposes, and lay all the groundwork, but is focused on generalizing a classical theorem. Then the second will focus on results more relevant to current topology, referencing results form the first but not weighed down by them.
My question is about what I should include in my setup at the beginning of the second article. I summarize a bunch of standard ideas at the beginning of my first article, which really does need to be there because it is not typical for someone working in any one of the fields to be familiar with the other concepts. I also introduce notation. Then in my second article I use all the same stuff, plus some more.
Is it okay to leave out a repetition of that background info, and refer the reader to my first article? I figure I should re-define any original or unusual notation, but I don’t want to have all that repetition in the first section of both articles. On the other hand, I want people to read the second one, and not be off-put by being referred to the first one, or feel the background is not well established.
Is there a standard protocol for writing a series of two or more articles that develop a concept continuously, which draw upon the same set of background definitions and theorems? Would it be better to just write one very long article after all?
Regardless of one’s opinion on the interest of my first article, there remains the general question of how to handle preliminary material in a series of articles on a niche topic. My third article might require the same set of foundational definitions and theorems. Do you list them each time? What do you do? Is there a good example of a respected author with a series of articles like this?