The cyclotomic trace and algebraic K-theory of spaces

  title={The cyclotomic trace and algebraic K-theory of spaces},
  author={Marcel B{\"o}kstedt and Wu-chung Hsiang and Ib Henning Madsen},
  journal={Inventiones mathematicae},
The cyclotomic trace is a map from algebraic K-theory of a group ring to a certain topological refinement of cyclic homology. The target is naturally mapped to topological Hochschild homology, and the cyclotomic trace lifts the topological Dennis trace. Our cyclic homology can be defined also for "group rings up to homotopy", and in this setting the cyclotomic trace produces invariants of Waldhausen's A-theory. Our main applications go in two directions. We show on the one hand that the K… 

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