Infinite families
This post is mostly a short complaint. Hopefully more math coming soon now that the semester is over. Low-dimensional topology can be hard, especially in dimension 4. As a result, pretty much every paper is of a "counterexample" structure (e.g. these manifolds are not diffeomorphic, this knot cannot bound a disk, etc). Such papers are made stronger (i.e. get into better journals) if you can give an infinite family of counterexamples to the problem. Sometimes, I really dislike this approach to papers (even though I am guilty of doing it because I still play the game). Let me explain just a couple feelings about it. - Usually there's no reason that this infinite family comprises all possible counterexamples and probably does not really narrow down the possibilities more than having one example, so it is basically answering the same question. (If it was expected this was the comprehensive list of counterexamples, then I would be stoked.) Since the idea for the