Mycroft, W. and Whitehouse, S. orcid.org/0000-0002-7896-506X (2021) The plethory of operations in complex topological K-theory. Annals of K-Theory, 6 (3). pp. 481-502. ISSN 2379-1683
Abstract
We provide a concrete introduction to the topologised, graded analogue of an algebraic structure known as a plethory, originally due to Tall and Wraith. Stacey and Whitehouse showed this structure is present on the cohomology operations for a suitable generalised cohomology theory. We compute an explicit expression for the plethory of operations for complex topological K-theory. This is formulated in terms of a plethory enhanced with structure corresponding to the looping of operations. In this context we show that the familiar lambda operations generate all the operations.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2021 Mathematical Sciences Publishers. First published in Annals of K-Theory in Vol. 6 (2021), No. 3 published by Mathematical Sciences Publishers. Reproduced here by permission of the publisher. This version is free to view and download for private research and study only. Not for re-distribution, re-sale, or use in derivative works. |
Keywords: | topological K-theory; K-theory operations; lambda operations; lambda ring; plethory |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Science (Sheffield) > School of Mathematics and Statistics (Sheffield) |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 24 Mar 2022 15:02 |
Last Modified: | 01 Apr 2022 07:53 |
Status: | Published |
Publisher: | Mathematical Sciences Publishers (on behalf of K-Theory Foundation, Inc.) |
Refereed: | Yes |
Identification Number: | 10.2140/akt.2021.6.481 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:185102 |