Determine homology nilpotency for the original-degree models

Determine the homology nilpotency Hnil(M_q) of the original-degree minimal Sullivan model M_q as a function of q, and establish whether the gap Hnil(M_q)-(3q-2) is unbounded.

Background

The paper proves that the original-degree model M_q has nil(M_q)=3q-2 and establishes the upper bound Hnil(M_q)≤4q-4. However, the lower-bound argument for the regraded models depends on separating cohomological degrees associated with different weights, so it cannot be directly transferred to M_q. The authors therefore leave open both the exact value of Hnil(M_q) and whether the quotient defect remains unbounded without regrading.

References

For the original degrees, what is $Hnil(M_q)$ as a function of $q$? In particular, is $Hnil(M_q)-(3q-2)$ unbounded?

— Unbounded Nilpotency Gaps on Rationally Elliptic Manifolds  (2610.21280 - Parent, 15 Oct 2026) in Section 5, “Further consequences and remaining questions”

In the present family, $nil=3q-2$ grows with $q$. Can the gap be unbounded while $nil$ remains fixed?

— Unbounded Nilpotency Gaps on Rationally Elliptic Manifolds  (2610.21280 - Parent, 15 Oct 2026) in Section 5, “Further consequences and remaining questions”

Can the degreewise finite spherical stabilization be replaced by a finite wedge, or the cone attachment by one cell?

— Unbounded Nilpotency Gaps on Rationally Elliptic Manifolds  (2610.21280 - Parent, 15 Oct 2026) in Section 5, “Further consequences and remaining questions”