Topological Hochschild and cyclic homology for Differential graded categories

Details Topological Hochschild and cyclic homology for Differential graded categories Topological Hochschild and cyclic homology for Differential graded categories

2008-04-17

arxiv.org/abs/0804.2791v2

Mathematics

Algebraic Topology

47 pages. Sections 10 and 11 are new

Scientific paper

We define a topological Hochschild (THH) and cyclic (TC) homology theory for differential graded (dg) categories and construct several non-trivial natural transformations from algebraic K-theory to THH(-). In an intermediate step, we prove that the homotopy theory of dg categories is Quillen equivalent, through a four step zig-zag of Quillen equivalences, to the homotopy theory of Eilenberg-Mac Lane spectral categories. Finally, we show that over the rationals two dg categories are topological equivalent if and only if they are quasi-equivalent.

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