On the formal group laws of unoriented and complex cobordism theory

1969/11/01 by Daniel Quillen · 5 citations
Mathematics · #Homotopy and Cohomology in Algebraic Topology #Algebraic structures and combinatorial models #Advanced Topics in Algebra #Cobordism #Mathematics #Formal group #Group (periodic table) #Law #Pure mathematics #Political science #Physics

paper · pdf · doi:10.1090/s0002-9904-1969-12401-8

openalex publication_date 1969/11/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/14

Abstract

In this note we outline a connection between the generalized cohomology theories of unoriented cobordism and (weakly-) complex cobordism and the theory of formal commutative groups of one variable [4], This connection allows us to apply Carrier's theory of typical group laws to obtain an explicit decomposition of complex cobordism theory localized at a prime p into a sum of Brown-Peterson cohomology theories [l] and to determine the algebra of cohomology operations in the latter theory.

Citations

• The Relation of Cobordism to K-Theories
• A spectrum whose Zp cohomology is the algebra of reduced pth powers

Cited by

• A Novice's guide to the adams-novikov spectral sequence
• Syntomic cohomology of truncated Brown--Peterson spectra
• Complex cobordism theory for number theorists
• Detecting exotic spheres in low dimensions using coker J
• Complex cobordism [wikipedia]