PomeRemark 22.1.4.C864B821AD8B Thanks to proposition 17.14.3, for any other $\theta '$ representing $\{ \theta \} $, we have a canonical bijection
\[ \mathrm{PSH}^{\mathrm{NA}}(X,\theta )\xrightarrow {\sim }\mathrm{PSH}^{\mathrm{NA}}(X,\theta '). \]
Moreover, these bijections satisfy the cocycle condition. If we view the set of closed real smooth $(1,1)$-forms representing $\{ \theta \} $ as a category with a unique morphism between any two objects, then we can define
\[ \mathrm{PSH}^{\mathrm{NA}}(X,\{ \theta \} )=\varprojlim _{\theta } \mathrm{PSH}^{\mathrm{NA}}(X,\theta ). \]
This definition is independent of the choice of the explicit representative of the cohomology class $\{ \theta \} $.
However, given the fact that our notation is already quite heavy, we stick to the set $\mathrm{PSH}^{\mathrm{NA}}(X,\theta )$. The constructions below are independent of the choice of $\theta $ within its cohomology class.
Comments
Corrections, questions, and mathematical discussion are welcome. Sign in with GitHub to comment. Comments are public.