In 2002 and 2003, Grigori Perelman posted two papers to the arXiv which claimed to provide a proof for William Thurston's geometrization conjecture, using Richard Hamilton's theory of Ricci flow.Perelman, Grisha. The entropy formula for the Ricci flow and its geometric applications. Perelman, Grisha. Ricci flow with surgery on three-manifolds. Perelman's papers attracted immediate attention for their bold claims and the fact that some of their results were quickly verified. However, due to Perelman's abbreviated style of presentation of highly technical material, many mathematicians were unable to understand much of his work, especially in his second paper. Beginning in 2003, Lott and Bruce Kleiner posted a series of annotations of Perelman's work to their websites, which was finalized in a 2008 publication.Kleiner, Bruce; Lott, John Notes on Perelman's papers. Geom. Topol. 12 (2008), no. 5, 2587–2855. Their article was most recently updated for corrections in 2013. In 2015, Kleiner and Lott were awarded the Award for Scientific Reviewing from the National Academy of Sciences of the United States for their work. Other well-known expositions of Perelman's work are due to Huai-Dong Cao and Xi-Ping Zhu, and to John Morgan and Gang Tian.Cao, Huai-Dong; Zhu, Xi-Ping. A complete proof of the Poincaré and geometrization conjectures—application of the Hamilton-Perelman theory of the Ricci flow. Asian J. Math. 10 (2006), no. 2, 165–492.Morgan, John; Tian, Gang. Ricci flow and the Poincaré conjecture. Clay Mathematics Monographs, 3. American Mathematical Society, Providence, RI; Clay Mathematics Institute, Cambridge, MA, 2007. xlii+521 pp.
