cohomology
cocycle
characteristic class
cochain cohomology
generalized (Eilenberg-Steenrod) cohomology
integral cohomology
K-theory
elliptic cohomology
tmf
complex cobordism
abelian sheaf cohomology
Deligne cohomology
etale cohomology
motivic cohomology
nonabelian cohomology
nonabelian groupoid cohomology
principal bundle
principal 2-bundle/gerbe
principal ∞-bundle
covering ∞-bundle/local system
∞-vector bundle
quantum anomaly
Spin structure
String structure
Fivebrane structure
Hochschild cohomology
Čech cohomology
equivariant cohomology
equivariant homotopy theory
Bredon cohomology
group cohomology
nonabelian group cohomology
Lie algebra cohomology
nonabelian Lie algebra cohomology
twisted cohomology
twisted bundle
twisted K-theory
twisted differential String- and Fivebrane structures
differential cohomology
differential generalized (Eilenberg-Steenrod) cohomology
differential nonabelian cohomology
differential equivariant cohomology
differential twisted cohomology
relative cohomology
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The material on gerbes is split into several sub-entries:
gerbe (as a stack)
gerbe (in nonabelian cohomology)
bundle gerbe
gerbe (general idea)