Top Journals For Geometry And Topology with Impact Factor, Citescore, Overall Ranking/Rating, h-index, SCImago Journal Rank (SJR), ISSN, Publisher, and other Important Details
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.
R. Ghrist, and A. Muhammad. IPSN '05: Proceedings of the 4th international symposium on Information processing in sensor networks, Piscataway, NJ, USA, IEEE Press, (2005)
M. Faloutsos, P. Faloutsos, and C. Faloutsos. Proceedings of the conference on Applications, technologies, architectures, and protocols for computer communication, volume 29 of SIGCOMM '99, page 251--262. New York, NY, USA, ACM, (October 1999)