An Elementary Classification of Symmetric 2-Cocycles

2008/11/25 by Adam Hughes, Hughes, Adam, JohnMark Lau +3
Mathematics · #18G35 #55N22 #Algebraic Topology (math.AT) #Commutative Algebra (math.AC) #FOS: Mathematics #math.AC #math.AT #msc:18G35 #msc:55N22

paper · pdf · doi:10.48550/arxiv.0811.4159

27 pages

arxiv created 2008/11/25 · arxiv updated 2009/12/01

Abstract

We present a classification of the so-called "additive symmetric 2-cocycles" of arbitrary degree and dimension over Z/p, along with a partial result and some conjectures for m-cocycles over Z/p, m > 2. This expands greatly on a result originally due to Lazard and more recently investigated by Ando, Hopkins, and Strickland, which together with their work culminates in a complete classification of 2-cocycles over an arbitrary commutative ring. The ring classifying these polynomials finds application in algebraic topology, including generalizations of formal group laws and of cubical structures.

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