This paper is an introduction and a survey to the concept of perfect isometries which was first introduced by Michel Broué in 1990. Our main aim is to provide proofs of numerous results scattered in the literature. On the other hand, we make some observations which did not appear anywhere before.
"Survey on perfect isometries." Rocky Mountain J. Math. 50 (5) 1517 - 1539, October 2020. https://doi.org/10.1216/rmj.2020.50.1517