Operations in connective K-theory

Vishik, Alexander; Merkurjev, Alexander

Abstract

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.

Citation

Vishik, A., & Merkurjev, A. (2023). Operations in connective K-theory. Algebra and Number Theory, 17(9), 1595–1636. https://doi.org/10.2140/ant.2023.17.1595

• 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
• DOI: https://doi.org/10.2140/ant.2023.17.1595
• Public URL: https://nottingham-repository.worktribe.com/output/14588784
• Publisher URL: https://msp.org/ant/2023/17-9/p03.xhtml