Complex point-like bounding cochains in obstructed dimensions

Construct point-like bounding cochains with complex coefficients in dimensions where the involution-compatible real point-like condition is obstructed, and determine whether compatibility with complex conjugation can produce analogous obstruction cancellations and relax the cohomological hypotheses required for their existence.

Background

When the dimension is congruent to zero modulo four, the real point-like condition is incompatible with the involution and the normalization of the boundary variable. The paper proposes using complex coefficients and the involution to seek cancellations analogous to those in the construction of real point-like bounding chains, with the aim of extending existence results to these remaining dimensions.

References

Moreover, in dimensions where the real point-like condition is obstructed, can one construct point-like bounding cochains with complex coefficients and use the involution to weaken the cohomological assumptions for their existence? The desired result would be analogous to Solomon--Tukachinsky's construction of real point-like bounding chains , in which the involution forces some obstruction classes to vanish and thereby relaxes the cohomological hypotheses. The question is whether a suitable compatibility with complex conjugation can yield similar cancellations in the remaining dimensions.

— Open WDVV equations for non-commutative families of bounding cochains  (2610.13209 - Kosloff, 9 Oct 2026) in Section 1, subsection “Open Gromov–Witten theory with an anti-symplectic involution” (Section 1.5)