Cobordisms in problems of algebraic topology

Виктор Матвеевич Бухштабер (К Семидесятилетию Со Дня Рождения)

“…Впоследствии Виктором Матвеевичем была построена общая теория двузначных формальных групп, ключевым результатом которой явилось вычисление универсальных одномерных двузначных формальных групп (см. [4], [5], [36]).…”

A survey of bordism and cobordism

“…Spin manifolds and Spin bordism There has been a continuing interest in Spin manifolds, for a number of reasons to be discussed here, since the work of Atiyah and Singer on the index of elliptic operators beginning in the early 1960s. If M n is a Spin manifold, assumed to be Riemannian, then in addition to the bundle FM ->• M of oriented orthonormal frames (with structure group 80 (21)), one has a bundle FM->M with structure group Spin(2Z) defining the Spin-structure on M, FM-+FM being a double cover. Making use of Clifford algebras [9], one has the complex half-spin representations S+ and S~ of Spin(2Z), and so also corresponding vector bundles, which we still write as S + and S~.…”

“…A survey of papers on cobordism theory published during the active decade from 1965 to 1975 has been made by V.M.Buchstaber [21]. The present survey is more restricted and personal, and is more in the nature of a narrative and guide to some of the major topics in this area.…”