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Operations in connective K-theory

Vishik, Alexander; Merkurjev, Alexander

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Alexander Merkurjev


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 ˆZ case. 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 ˆZ-coefficients are topologically generated by stable multiplicative operations. This is not true for integral operations.

Journal Article Type Article
Acceptance Date Oct 4, 2022
Online Publication Date Sep 9, 2023
Publication Date Sep 9, 2023
Deposit Date Dec 21, 2022
Publicly Available Date Sep 9, 2023
Print ISSN 1937-0652
Electronic ISSN 1944-7833
Peer Reviewed Peer Reviewed
Volume 17
Issue 9
Pages 1595–1636
Public URL
Publisher URL


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