group cohomology, nonabelian group cohomology, Lie group cohomology
cohomology with constant coefficients / with a local system of coefficients
differential cohomology
Non-connective algebraic K-theory, sometimes called Bass K-theory, is a variant of algebraic K-theory with non-trivial homotopy groups/cohomology groups in negative degrees.
This universally arises as the hom-spectra in the (∞,1)-category of noncommutative motives.
A review and further discussion is in (Blumberg-Gepner-Tabuada 10, section 9).
geometric context | universal additive bivariant (preserves split exact sequences) | universal localizing bivariant (preserves all exact sequences in the middle) | universal additive invariant | universal localizing invariant |
---|---|---|---|---|
noncommutative algebraic geometry | noncommutative motives $Mot_{add}$ | noncommutative motives $Mot_{loc}$ | algebraic K-theory | non-connective algebraic K-theory |
noncommutative topology | KK-theory | E-theory | operator K-theory | … |
The characterization of non-connective algebraic K-theory via noncommutative motives is due to
Mathematica 147 (2011), 1281–1320 (arXiv:0903.3717)
and further expanded on in section 9 of
Last revised on January 5, 2015 at 17:36:34. See the history of this page for a list of all contributions to it.