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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Products and duality in Waldhausen categories


Authors: Michael S. Weiss and Bruce Williams
Journal: Trans. Amer. Math. Soc. 352 (2000), 689-709
MSC (1991): Primary 57N99, 57R50, 19D10
Published electronically: October 5, 1999
MathSciNet review: 1694381
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Abstract: The natural transformation $\Xi $ from $\mathbf{L}$-theory to the Tate cohomology of $\mathbb{Z}/2$ acting on $\mathbf{K}$-theory commutes with external products. Corollary: The Tate cohomology of $\mathbb{Z}/2$ acting on the $\mathbf{K}$-theory of any ring with involution is a generalized Eilenberg-Mac Lane spectrum, and it is 4-periodic.


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Additional Information

Michael S. Weiss
Affiliation: Department of Mathematics, University of Aberdeen, Aberdeen AB24 3UE, U.K.
Email: m.weiss@maths.abdn.ac.uk

Bruce Williams
Affiliation: Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 46556
Email: williams.4@nd.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-99-02552-0
PII: S 0002-9947(99)02552-0
Keywords: Products, ring spectrum, Tate cohomology, surgery
Received by editor(s): January 9, 1997
Published electronically: October 5, 1999
Additional Notes: Both authors supported in part by NSF grant.
Article copyright: © Copyright 1999 American Mathematical Society