In 2002 and 2003, Grigori Perelman posted three papers on the arXiv which purported to prove the Poincaré conjecture and Geometrization conjecture in the field of three-dimensional geometric topology. Perelman's papers were immediately acclaimed for many of their novel ideas and results, although the technical details of many of his arguments were seen as hard to verify. In collaboration with John Morgan, Tian published an exposition of Perelman's papers in 2007, filling in many of the details. Other expositions, which have also been widely cited, were written by Huai-Dong Cao and Xi-Ping Zhu, and by Bruce Kleiner and John Lott. In collaboration with Nataša Šešum, Tian also published an exposition of Perelman's work on the Ricci flow of Kähler manifolds, which Perelman did not publish in any form. Eight years after the publication of Morgan and Tian's book, Abbas Bahri, in his article "Five gaps in mathematics," pointed to some of their work as being in error. This was amended by Morgan and Tian.