Topological Hochschild and cyclic homology for Differential graded categories
Algebraic Topology
2014-10-01 v2 K-Theory and Homology
Abstract
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.
Cite
@article{arxiv.0804.2791,
title = {Topological Hochschild and cyclic homology for Differential graded categories},
author = {Goncalo Tabuada},
journal= {arXiv preprint arXiv:0804.2791},
year = {2014}
}
Comments
47 pages. Sections 10 and 11 are new