Equivalence of the spectral sequence with Borman–Sheridan–Varolgunes

Determine whether the q-filtration spectral sequence SH^*(M\setminus D)[q] ⇒ SH^*_q(M,D) constructed in this paper coincides with the spectral sequence of Borman–Sheridan–Varolgunes, and if so, provide an explicit identification; otherwise, characterize the differences.

Background

The authors recover the Borman–Sheridan–Varolgunes (BSV) result after inverting q but explicitly note uncertainty whether their spectral sequence agrees with BSV’s. Establishing equivalence (or identifying differences) would clarify the relationship between the approaches and solidify the connection to the deformation of symplectic cohomology towards quantum cohomology.

This comparison is important for understanding the generality and robustness of spectral-sequence methods in relating symplectic cohomology of complements to the cohomology of the ambient manifold via divisor data.