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Dual calculus for functors to spectra. (English) Zbl 0996.19005

Greenlees, J. P. C. (ed.) et al., Homotopy methods in algebraic topology. Proceedings of an AMS-IMS-SIAM joint summer research conference, University of Colorado, Boulder, CO, USA, June 20-24, 1999. Providence, RI: American Mathematical Society (AMS). Contemp. Math. 271, 183-215 (2001).
Author’s abstract: We construct a theory formally dual to Goodwillie’s calculus of functors for functors which take values in spectra. We then show that the two theories are essentially equivalent for endofunctors of spectra when particular obstruction groups obtained from Tate cohomology vanish. We apply this fact to show that a particular coTower for rational algebraic \(K\)-theory is as effective but no more effective than its dual counterpart – negative cyclic homology.
For the entire collection see [Zbl 0964.00013].

MSC:

19D55 \(K\)-theory and homology; cyclic homology and cohomology
55P42 Stable homotopy theory, spectra
18F25 Algebraic \(K\)-theory and \(L\)-theory (category-theoretic aspects)
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