Abstract
For a discrete ring, a simplicial –bimodule, and a simplicial set, we construct the Goodwillie Taylor tower of the reduced –theory of parametrized endomorphisms as a functor of . Resolving general –bimodules by bimodules of the form , this also determines the Goodwillie Taylor tower of as a functor of . The towers converge when or is connected. This also gives the Goodwillie Taylor tower of as a functor of .
For a functor with smash product and an –bimodule , we construct an invariant which is an analog of with coefficients. We study the structure of this invariant and its finite-stage approximations and conclude that the functor sending is the –th stage of the Goodwillie calculus Taylor tower of the functor which sends . Thus the functor is the full Taylor tower, which converges to for connected X.
Citation
Ayelet Lindenstrauss. Randy McCarthy. "On the Taylor tower of relative $K$–theory." Geom. Topol. 16 (2) 685 - 750, 2012. https://doi.org/10.2140/gt.2012.16.685
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