Сборник работ по теории гомологии / Академия наук Грузинской ССР ; Труды Тбилисского ордена Трудового Красного Знамени математического института имени А. М. Размадзе, том XLI ; редактор тома Г. С. Чогошвили ; председатель редакционной коллегии Н. И. Мусхелишвили.
Тбилиси : Мецниереба, 1972. 165 страниц ; 25 см. Тираж 1000 экземпляров. Мягкая обложка.
Состояние: обложка хорошее: заломы, небольшая утрата у нижнего края корешка, следы старых сгибов на задней стороне. Блок хороший: текст полный и чистый, скрепление прочное.
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Collected Works on Homology Theory / Academy of Sciences of the Georgian SSR ; Proceedings of the Tbilisi A. M. Razmadze Mathematical Institute, Order of the Red Banner of Labour, vol. XLI ; volume editor G. S. Chogoshvili ; chairman of the editorial board N. I. Muskhelishvili.
Tbilisi : Metsniereba, 1972. 165 pp. ; 25 cm. Print run of 1000 copies. Paperback.
Condition: wrapper good: creasing, minor loss at the lower spine edge, old fold marks to the rear cover. Text block good: text complete and clean, binding firm.
A landmark collection in the Tbilisi school of algebraic topology, issued under the chairmanship of Nikoloz Muskhelishvili, the founding figure of the Georgian Academy of Sciences and one of the most eminent applied mathematicians of the twentieth century, and edited by Giorgi Chogoshvili, whose own work bridged the Alexandrov-Čech and Steenrod approaches to homology theory. As the volume's own annotation states, this is the first complete published exposition of Kolmogorov's 1936 homology theory, whose original results had appeared only as brief, unproven notes; Meliton Balavadze's opening paper reconstructs the theory in the modern language of algebraic topology and extends several of Kolmogorov's propositions, showing among other results that Steenrod's homology theory for any coefficient domain is isomorphic to one of Kolmogorov's variants. The collection continues with David Baladze on generalized Steenrod homology groups, Meer Bokshtein - whose name is permanently attached to the Bockstein homomorphism and spectral sequence fundamental to modern algebraic topology - on the tensor product functor for abelian groups in abelian categories, Alexander Zarelua on the cohomological structure of finite-multiplicity mappings, Khariton Inasaridze on exact homology, and Lasha Mdzinarishvili on the equivalence of the Kolmogorov and Steenrod homology theories, with English summaries of all six papers appended. Printed in a run of 1000 copies, the volume documents the Razmadze Institute's central contribution to Soviet algebraic topology at a moment when several of its authors - Bokshtein and Chogoshvili chief among them - were figures of international standing in the field.