Symmetric operations in Algebraic Cobordisms, by Alexander Vishik

In this article we introduce certain new, so-called, symmetric cohomological operations in algebraic cobordism of smooth quasiprojective varieties, and describe various properties of them. We establish connection to the Landweber-Novikov operations, and demonstrate on examples, that symmetric operations sometimes work, where Landweber-Novikov operations do not (related to 2-torsion effects). Symmetric operations also provide the natural obstructions for the cobordism class to be represented by the embedding.

The original March 1, 2006, has been replaced on April 7 with an updated version.

Alexander Vishik <>