Christos Papakyriakopoulos

Christos Papakyriakopoulos ( Greek Χρίστος Παπακυριακόπουλος , * 1914 in Chalandri , Athens ; † June 29, 1976 ) was a Greek mathematician who dealt with geometric topology .

Life

Papakyriakopoulos ("Papa" for short, as he was usually called) was the son of a wealthy businessman and studied at the Metsovion Polytechnic from 1933 with the aim of becoming an engineer. Under the influence of the mathematics professor Nikolaos Kritos, he switched to studying mathematics at the University of Athens, where he received his doctorate in 1943. He specialized in topology, which he mainly learned in self-study (especially the textbook by Pawel Alexandrow and Heinz Hopf Topologie from 1935). The reviewer for his dissertation was Constantin Carathéodory , since topology specialists did not exist in Greece at the time . In his dissertation he gave a new proof (after James Waddell Alexander ) of the topological invariance of the homology groups of simplicial complexes. In 1944 he went to the country during the civil war , taught there and joined the communist national liberation movement, while his brother fought (and fell) on the other side at the same time. Therefore he had to leave the Polytechnic in 1946 like his professor Kritos, whose (unpaid) assistant he had previously been at the Polytechnic.

He is known for his proof of Dehn's lemma in the geometric topology of 3-manifolds, which previously had a long history of unsuccessful attempts at proof. Max Dehn believed he had proven it in 1910, but Hellmuth Kneser found a loophole. The first proof of "Papa" in 1948 was false, but got him an invitation from Ralph Fox to Princeton (he had given Fox the proof by letter from Greece). "Papa" came to Princeton in 1948 and never returned (except for a brief visit in 1952 at his father's funeral). Fox made sure that he could research undisturbed in Princeton and also shielded him from claims by the Greek security authorities, who were expelling him from the USA as communists in the McCarthy era. From 1955 to 1958 he was at the Institute for Advanced Study . In 1959 he became a Sloan Research Fellow . He later stayed in Princeton and lived a rather withdrawn and Spartan life. For decades he concentrated his energies on proving the Poincaré conjecture , which Grigori Perelman succeeded in doing much later . He was considering a visit to Greece after the military junta was overthrown in 1975, but before that he died of stomach cancer.

He served as a model for the mathematical hermit Uncle Petros in the novel "Uncle Petros and the Goldbach Hypothesis" by Apostolos Doxiadis .

Act

In knot theory , knots (mappings of the circle into three-dimensional manifolds ) were characterized by Dehn by algebraic invariants ( knot group ) in 1910 , and Dehn's lemma was important for his proof that knots with the same algebraic invariants as the trivial knot (i.e. the one not knotted Loop) were actually deformed in these and thus "dissolvable". The proof of Dehn's lemma was given by "Papa" with his new "tower construction" in 1956, at the same time he found generalizations of the lemma in the loop theorem and the theorem of spheres , also fundamental theorems in the geometric topology of 3-manifolds. In 1954 he lectured on this as an invited speaker at the Annual Meeting of the AMS in Ohio and in 1964 he received the first Oswald Veblen Prize for it . In 1958 he was invited speaker at the International Congress of Mathematicians in Edinburgh ( The theory of three dimensional manifolds since 1950 ).

Web links

• Papastavridis' biography, with an explanation of his work
• Dehn's lemma in Mathworld

References

1. ↑ Papakyriakopoulos A New Evidence for the Invariance of the Homology Group of a Complex , (Greek) Bulletin of the Greek Math. Society, Vol. 22, 1946, pp. 1–154
2. ↑ Dehn About the topology of three-dimensional space ( Memento of the original from January 26, 2016 in the Internet Archive ) Info: The archive link was automatically inserted and not yet checked. Please check the original and archive link according to the instructions and then remove this notice. , Mathematische Annalen, Vol. 69, 1910, pp. 137-168 
3. ↑ On Dehn's Lemma and the Asphericity of Knots , Proc. Nat. Acad. Sciences, Vol. 43, 1957, p. 169, online here PNAS , detailed Annals of Mathematics, Vol. 66, 1957, pp. 1-26
4. ^ "On solid tori", Proceedings London Math. Soc., Series III, Vol. 7, 1957, pp. 281-299. The evidence was refined from John Stalling's On the loop theorem , Annals of Math., Vol. 72, 1960, pp. 12-19.
5. ↑ proved in the same work as Dehn's lemma. Improved by JHC Whitehead On the sphere in 3-manifolds , Bull. AMS, Vol. 64, 1958, pp. 161-166.
6. ↑ Some problems on 3-dimensional manifolds , published in Bull. American Math. Soc., Vol. 64, 1958, pp. 317-335.