# nLab M M Postnikov

Михаил Михайлович Постников, (that is Mihail Mihajlovič Postnikov (in a slavistic transliteration as in ISO9 or G. Shevelov, A prehistory of Slavic, Columbia 1965) or Mikhail Mikhailovich Postnikov) is a former Russian (Soviet) topologist (27.10.1927–27.5.2004) and a professor at MGU until his sudden death.

His thesis under the mentorship of L. S. Pontrjagin (ru.wiki), contained a construction of a homotopical decomposition of a topological space into a tower of fibrations (now called a Postnikov tower) and cohomological invariants (Postnikov invariants) which together with the tower form a “system” (Postnikov system). The use of these data enabled him to effectively encode the full homotopy type of a space.

After his early work, Postnikov dedicated himself to teaching, leading a famous seminar at MGU, and advising students (among most successful of his students is Rudyak) and largely neglected his own research. As a clear and superb lecturer, he also wrote several volumes of advanced textbooks in geometry and topology, and a booklet on Galois theory. Unfortunately, he also dedicated much of his efforts and time to an alternative history, considered pseudoscience by the mainstream. Some of his mathematical memoirs may be found in the book Golden Years of Moscow Mathematics, by Smilka Zdravkovska (AMS, 2nd ed. 2007).

• M. M. Postnikov, Issledovaniya po gomotopičeskoĭ teorii nepreryvnyh otobraženiĭ. I. Algebraičeskaya teoriya sistem. II. Naturalʹnaya sistema i gomotopičeskiĭ tip. (Russian) $[$Investigations in homotopy theory of continuous mappings. I. The algebraic theory of systems. II. The natural system and homotopy type.$]$ Trudy Mat. Inst. Steklov. no. 46. Izdat. Akad. Nauk SSSR, Moscow, 1955. (mathnet:tm1182)