Is it a problem that I haven't made any arrangements with a publisher?

Nowadays, you don't necessarily need a publisher to publish your work.
You can post it on your homepage yourself or email it to interested colleagues. In addition, almost every higher education institution has a repository you can add your publication to. Another option is to post your work on relevant websites. You therefore don't need any arrangements with a publisher to share your work with the public. In some cases, however, for example if you want to publish your work in a certain journal or publish a book in a certain series, you will have to make certain arrangements with a publisher. You can limit these arrangements to a single publication via that single medium.