• A
  • A
  • A
  • ABC
  • ABC
  • ABC
  • А
  • А
  • А
  • А
  • А
Regular version of the site

Working paper

On the Structure of Algebraic Cobordism

Sechin P.
In this paper we investigate the structure of algebraic cobordism of Levine-Morel as a module over the Lazard ring with the action of Landweber-Novikov and symmetric operations on it. We show that the associated graded groups of algebraic cobordism with respect to the topological filtration Ω∗_(r)(X) are unions of finitely presented 𝕃-modules of very specific structure. Namely, these submodules possess a filtration such that the corresponding factors are either free or isomorphic to cyclic modules 𝕃/I(p,n)x where deg x≥p^n−1/(p−1). As a corollary we prove the Syzygies Conjecture of Vishik on the existence of certain free 𝕃-resolutions of Ω∗(X), and show that algebraic cobordism of a smooth surface can be described in terms of K_0 together with a topological filtration.