Speciality:
01.01.04 (Geometry and topology)
Birth date:
1.12.1949
Keywords: operads; homology and homotopy groups; spectral sequence.
Subject:
The field of scientific interests includes Operad Theory and its applications to determine the homotopy type of topological spaces, describing the Adams spectral sequence, calculation the homology groups of iterated loop spaces and the homotopy groups of spheres. The operad theory for the category of chain complexes is constructed. It is proved that the $E_\infty$-coalgebra structure on the singular chain complex of a 1-connected topological space determines the weak homotopy type of the spaces. The $E_2$- term of the Adams spectral sequence is described. The homology of iterated loop spaces over the real and complex projective spaces are calculated. The $E_\infty$- structure on the Adams spectral sequence is described. Some higher differentials of this spectral sequence are calculated.
Main publications:
Smirnov V. A., “A general algebraic approach to the problem of describing the second term of the Adams spectral sequence of stable homotopy groups of spheres”, Tensor and Vector Analisis, Gordon and Breach Science Publishers, Amsterdam, 1998, 213–250
Smirnov V. A., “Bioperady i bialgebry Khopfa v teorii kobordizmov”, Matematicheskie zametki, 65:2 (1999), 270–279
Smirnov V. A., “Algebra Daiera–Lashofa i algebra Stinroda dlya obobschennykh gomologii i kogomologii”, Matematicheskii sbornik, 190:12 (1999), 93–128
Smirnov V. A., “$A_\infty$-struktury i funktor $\mathscr D$”, Izvestiya RAN, ser. matem., 64:5 (2000), 148–162
Smirnov V. A., Simplicial and operad methods in algebraic topology, Transl. Math. Monogr., 198, American Mathematical Society, Providence, RI, 2001, 235 pp.
