A Chiang-type lagrangian in $$mathbb {CP}^2$$

We analyse a monotone lagrangian in (mathbb {CP}^2) that is hamiltonian isotopic to the standard lagrangian (mathbb {RP}^2), yet exhibits a distinguishing behaviour under reduction by one of the toric circle actions, namely it intersects transversally the reduction level set and it projects one-to-one onto a great circle in (mathbb {CP}^1). This lagrangian thus provides an example of embedded composition fitting work of Wehrheim–Woodward and Weinstein.