Donaldson divisors and spectral invariants

We establish a comparison between spectral invariants for a symplectic manifold and a Donaldson divisor therein, and answer a question of Borman from 2012 on the reduction of Entov–Polterovich quasimorphisms, under a reasonable assumption. The method involves a quantitative interpretation of Biran–Khanevsky’s quantum Gysin sequence.