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Publication policy

Monday, 21 December, 05:12, posic.livejournal.com
Basically, there are two kinds of research texts in mathematics: those that are easy to ignore and those that are difficult to ignore. To take an obvious example, something called "Inter-Universal Teichmueller Theory" was probably very easy to ignore for as long as it did not claim much applications. Once it claimed a proof of the ABC conjecture, it became much harder to ignore.

Or, to bring some examples from my own work, a preprint called "Contraherent cosheaves" is very easy to ignore for almost everyone. It does not stand in the way of anybody's research aspirations or claims to competence, certainly not yet. Whoever reads it, probably does so because he thinks this piece of math is important in itself or learning it would advance his research goals, but not because he has to.

Likewise, my book on semi-infinite homological algebra was and remains very easy to ignore for almost everybody, except perhaps the very few people working specifically in the narrow area of semi-infinite cohomology of associative algebras. Even specialists in comodules seem to have paid attention to contramodules only inasmuch as they found them easy and pleasant to play with, but not that they had to (and the attention turned out to be very limited in the end).

When, as it happens once in a while, I put a paper on the arXiv proving a disproving a known conjecture, or clearly improving upon somebody's recently published results, or offering a definitive treatment of foundations of a recently popular research area, etc., this is harder to ignore.

So, I think that texts that are easy to ignore as preprints do not become harder to ignore when they have been peer reviewed and published; certainly not significantly harder. Publishing my manuscript on semi-infinite homological algebra as a monograph in one of the more obscure Birkhauser series did very little to improve its fate. It may have worked to solidify the problem this piece of work represents for the very small related community, but otherwise the effect is very limited. Noone reads this book.

If anybody wanted to, he could just as well read it as an arXiv preprint. As, indeed, some people seem to have read parts of the "Contraherent cosheaves" manuscript, which of course remains just an unpublished arXiv preprint for a number of years already.

On the other hand, texts that are not easy to ignore as preprints may become yet much harder to ignore once they have been peer-reviewed and published in journals that, while perhaps not being very prestigious or "high level", offer a reasonably solid guarantee of overall correctness of what they print. Like, a proof of the ABC conjecture published in Journal of Number Theory may or may not advance the author's career as much as the same proof published in Annals of Mathematics would; but it would certainly present enough of a problem for the people positioning themselves as specialists in the area, in the sense of them being forced to acquire a certain degree of command of the content of such work irrespectively of whether they like it or not.

This will get them classified into those who can learn and those who can't, with the former receiving an advantage over the latter, which is the larger goal overall.

Hence, the general direction of a paper submission and publication strategy for somebody who just wants to force the world of so-called professional researchers to recognize and learn what he believes are his deep and important ideas seems to be clear. Whatever is easy to ignore, may as well remain arXiv preprints, to be worked on and built up as a way to acquire understanding of fundamental questions by the author himself and whatever dedicated readership he is lucky to get. Whatever is not easy to ignore (and you've got to produce such work once in a while if you do not want to remain forever ignored) should be published in journals or book series of solid reputation in the sense of their reviewing process offering a reasonable guarantee of the work being meaningful and largely correct.

As to the prestigious journals so proud of their high quality levels, i.e., the ones that the authors generally use to advance their careers in terms of obtaining tenure etc., these should be caught red-handed negligently rejecting good work and boycotted ever since, first of all in terms of rejecting their requests to review. Unless, of course, it turns out that some of them do not reject good work negligently, in which case they indeed deserve our cooperation as reviewers as well as authors.
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