I am a mathematics PhD student in the Western world.
I have a (single author) preprint in mathematics that I think will help my postdoc applications a lot. I wrote up the preprint about a month back, and gave it to my advisor for corrections. They did not have time for corrections as they were busy with their other duties. I asked them whether I could post it on arXiv, circulate it amongst people I want to work with, put it up on my website, etc. They asked me not to, as it might contain mistakes, which might be more embarrassing. However, I have job applications due in a couple of weeks, and really want to add this paper to my portfolio.
They have now read it and verified the accuracy of the results, although the paper might still need some re-structuring, etc. Is it now ethical to distribute it amongst my future employers, recommendation letter writers, etc without asking them?
I could of course just ask them, but I feel that they might not want me to do it, as their style is to only circulate extremely polished work, etc. However, for making myself more employable, and also because the paper is really my intellectual property and I should be free to do whatever I want, I do want to circulate it and share my results.
I know it is legal for me to circulate my work, as it is my property. But is it ethical? I don't agree with my advisor's assessment that I should suppress my work, and that they can mention it in their letter without me putting out my work.
Will it burn bridges with them to circulate it? I am not yet posting it on arXiv, as I feel that will be too incendiary, but I do perhaps want to share it with the schools I am applying to.