Speciality:
01.01.04 (Geometry and topology)
Birth date:
3.08.1935
Keywords: compactification theory,
homological dimension,
locally compact groups and coset spaces,
sheaves in homology and cohomology theory,
homological methods in topological problems,
spectral sequences,
hyperhomology,
general forms of Poincare duality,
homological and cohomological multiplications,
limit passages and inverse limit derived functors,
relative homological algebra,
de Rahm cohomology with locally constant coefficients.
Subject:
Modern methods of homology and cohomology theory applications to various problems in general topology are presented. These methods are based on the wide usage of the sheaf theory apparatus and adequate means of homological algebra. Among examined problems there are various homological characteristics of the dimension, the behaviour of the dimension, under various continuous mappings, homological type conditions for spreads of homeomorphisms and some mappings on suitable compactifications of topological spaces, special sort compactifications, homological locally connected spaces and generalized manifolds, general forms and categorical nature of Poincare duality, a common construction of (co)homological product operations, common categorical nature of suitable filtrations in homology of topological spaces, homological structures of mappings and adequate spectral sequences, limit passages in homology theory, axiom problems for (co)homology groups and homological products. Homological algebra constructions reflecting the general categorical nature of various relations of homological type in topology are also presented.
Main publications:
Sklyarenko E. G. K teorii obobschennykh mnogoobrazii // Izvestiya AN SSSR, ser. matem., 1971, 35(4), 831–843.
Sklyarenko E. G. Otnositelnaya gomologicheskaya algebra v kategorii modulei // Uspekhi matem. nauk, 1978, 33(3), 85–120.
Sklyarenko E. G. Gomologii i kogomologii obschikh prostranstv // VINITI, Itogi nauki i tekhniki, sovremennye problemy matematiki, fundamentalnye napravleniya, 1989, 50, 129–266.
Sklyarenko E. G. O prirode gomologicheskikh umnozhenii dvoistvennosti // Uspekhi matem. nauk, 1994, 49(1), 141–198.
Sklyarenko E. G. Giper(ko)gomologii dlya tochnykh sleva kovariantnykh funktorov i teoriya gomologii topologicheskikh prostranstv // Uspekhi matem. nauk, 1995, 50(3), 109–146.
