Isometry Group of Gromov--Hausdorff Space (1806.02100v2)

Abstract: The present paper is devoted to investigation of the isometry group of the Gromov-Hausdorff space, i.e., the metric space of compact metric spaces considered up to an isometry and endowed with the Gromov-Hausdorff metric. The main goal is to present a proof of the following theorem by George Lowther (2015): The isometry group of the Gromov-Hausdorff space is trivial. Unfortunately, the author himself has not publish an accurate text for 2 years passed from the publication of draft (that is full of excellent ideas mixed with unproved and wrong statements) in the https://mathoverflow.net/ blog (see the exact reference in he bibliography).