Review of key concepts in topology, with a view towards analogues for schemes. Homotopy theory and representability. See concept note.
Chromatic homotopy theory.
For versions of K-theory for topological spaces, see the headings treating K-theory below.
An introduction to cohomology by Tillmann: link
Many versions! Include maybe Cubical cohomology.
There is something by Beilinson/Drinfeld, some axioms I think, maybe related to factorization algebras, and maybe BRST cohomology?
Homotopy type, Homotopy groups
Bordism, Complex cobordism, Elliptic cohomology, Brown-Peterson cohomology, Morava K-theory, Morava E-theory, Johnson-Wilson cohomology
Alexander-Spanier cohomology, Cellular homology
nLab page on B40 Some algebraic topology