Lev Semёnovič Pontrjagin (Лев Семёнович Понтрягин) was an influential Soviet mathematician working in Moscow. His main works till the late 1940s were in topology, especially the study of topological groups (including study of Pontrjagin duality) and algebraic topology in which he also explored applications of differentiable manifolds for computation of homotopy groups; including the introduction of framed cobordism in that work. After the success of the French mathematical school in the late 1940s in introducing new methods of sheaf theory, which Pontrjagin did not like as less direct than the more intuitive geometric methods he was master of, and after some pressure from the government, Pontrjagin switched into applied mathematics where he did some fundamental work, especially in optimization theory.
Pontrjagin was a full member of the (Soviet) Academy of Sciences. He was blind since the age of 14.
ON smooth manifolds in homotopy theory (Thom collapse/Cohomotopy charge, cobordisms):
Introducing the Pontrjagin product:
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