My earlier posts about using Vim were well received and it’s about time for an update. I’ve been doing a lot more work with Vim lately and have spent some time configuring my workflow for peak efficiency, so here’s a snapshot of my current state.
You know the routine. You come across a topological space X and you need to find its fundamental group. Unfortunately, X is an unfamiliar space and it's too difficult to look at explicit loops and relations. So what do you do? You look for another space Y that is homotopy equivalent to X and whose fundamental group is much easier to compute. And voila! Since X and Y are homotopy equivalent, you know that the fundamental group of X is isomorphic to the fundamental group of Y. Mission accomplished. Below is a list of some homotopy equivalences which I think are pretty clever and useful to keep in your back pocket for, say, a qualifying exam or some other pressing topological occasion.
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V. Mazurov, and E. Khukhro. (2014)cite arxiv:1401.0300Comment: A few new solutions and references have been added. Preparation of the next 19th issue is underway, new problems are welcome, as well as comments on previous editions.