… modules over S-algebras. Examples studied include real and complex K-theory, both
connective and periodic. … The category of crt-acyclic crt-modules has enough projectives and all …

… of a C-algebra to periodic cyclic homology; we emphasize algebras … A differentiable G-module
is a complex vector space V, … Hence it suffices to show that this latter complex is acyclic. …

… how to construct chain complexes of K[u] modules whose homology is … to give periodic double
complexes, the b, B complex of … The proof of associativity follows the basic acyclic models …

… modules over S-algebras. Examples studied include real and complex K-theory, both
connective and periodic. … The category of crt-acyclic crt-modules has enough projectives and all …

… We get easily that every acyclic complex of injective R-modules … acyclic complex I of injective
modules is Ding injective in \(\mathrm{Ch}(R)\). Now let J be any FP-injective chain complex…

… We will now use the results from the previous section to study projective n–complexes over
groups with periodic cohomology. By Proposition 5.1, this will lead to a proof of the following …

… complex obtained from the Loday-Quillen cyclic bi-complex and S the periodicity map on the
level of complexes (… example of a 1-summable Fredholm module, but before we present this …

… K-flat to other classes of complexes, in the form of the following (periodic) diagram of triangulated
… R ( C , X ) is acyclic for any acyclic complex of pure-projective modules C; we call these …

… -periodic A ∞ -category C S , st . (It is the twisted complexes in a particularly simple two-periodic …
We could equivalently assume our morphisms form Z / 2 Z -graded k-modules. Then the …

… , and secondly to negative cyclic and periodic cyclic homology. In … Besides mixed complexes
we also consider S-modules, … we can argue by induction that Horn,, (M, N/F”N) is acyclic for …