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arXiv · 1309.5644

Symmetric operations for all primes and Steenrod operations in Algebraic Cobordism

Alexander Vishik
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Abstract

In this article we construct Symmetric operations for all primes (previously known only for p=2). These unstable operations are more subtle than the Landweber-Novikov operations, and encode all p-primary divisibilities of characteristic numbers. Thus, taken together (for all primes) they plug the gap left by the Hurewitz map L ---> Z[b_1,b_2,...], providing an important structure on Algebraic Cobordism. Applications include: questions of rationality of Chow group elements - see [11], and the structure of the Graded Algebraic Cobordism. We also construct Steenrod operations of T.tom Dieck-style in Algebraic Cobordism. These unstable multiplicative operations are more canonical and subtle than Quillen-style operations, and complement the latter.

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Alexander Vishik. 2013-09-22. Symmetric operations for all primes and Steenrod operations in Algebraic Cobordism. https://doi.org/10.1112/s0010437x15007757

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