2020/06/22 by Alexander Merkurjev, Merkurjev, Alexander, Alexander Vishik +1
Mathematics · #19L20 #19L41 #55S25 #Advanced Topics in Algebra #Advanced Topology and Set Theory #Algebraic Geometry (math.AG) #Algebraic Topology (math.AT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT)
paper · pdf · doi:10.48550/arxiv.2006.12193
openalex publication_date 2020/06/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this article we classify additive operations in connective K-theory with various torsion-free coefficients. We discover that the answer for the integral case requires understanding of the ℤ one. Moreover, although integral additive operations are topologically generated by Adams operations, these are not reduced to infinite linear combinations of the latter ones. We describe a topological basis for stable operations and relate it to a basis of stable operations in graded K-theory. We classify multiplicative operations in both theories and show that homogeneous additive stable operations with ℤ-coefficients are topologically generated by stable multiplicative operations. This is not true for integral operations.