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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Integer-valued polynomials and $ K$-theory operations


Authors: M-J. Strong and Sarah Whitehouse
Journal: Proc. Amer. Math. Soc. 138 (2010), 2221-2233
MSC (2010): Primary 55S25; Secondary 13F20, 11B73
Published electronically: January 29, 2010
MathSciNet review: 2596063
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Abstract: This paper provides a unifying approach to recent results linking the fields of integer-valued polynomials and operations in $ K$-theory. Following work of Bhargava, we set up a general framework encompassing several examples of rings of integer-valued polynomials. Our main results give bases for the duals of these rings. The rings and their duals all arise in topology as various kinds of cooperations and operations in complex $ K$-theory. We show how several previously understood examples fit into this framework and we present some new examples.


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Additional Information

M-J. Strong
Affiliation: Department of Pure Mathematics, University of Sheffield, Sheffield S3 7RH, United Kingdom

Sarah Whitehouse
Affiliation: Department of Pure Mathematics, University of Sheffield, Sheffield S3 7RH, United Kingdom
Email: s.whitehouse@sheffield.ac.uk

DOI: http://dx.doi.org/10.1090/S0002-9939-10-10237-8
PII: S 0002-9939(10)10237-8
Keywords: $K$-theory, cohomology operations, integer-valued polynomials
Received by editor(s): May 5, 2009
Received by editor(s) in revised form: September 9, 2009
Published electronically: January 29, 2010
Communicated by: Brooke Shipley
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.