If a compact ANR is a Gromov-Hausdorff limit of closed n-manifolds with bounded contractibility functions, then it is an open cell-like image of each sufficiently close approximating manifold, resolving Moore's conjecture in this setting.
Stability, Finiteness and Dimension Four
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
We prove that for any $k\in \mathbb{R},$ $v>0,$ and $D>0$ there are only finitely many diffeomorphism types of closed Riemannian $4$-manifolds with sectional curvature $\geq k,$ volume $\geq v,$ and diameter $\leq D.$
citation-role summary
background 1
citation-polarity summary
fields
math.MG 1years
2025 1verdicts
CONDITIONAL 1roles
background 1polarities
unclear 1representative citing papers
citing papers explorer
-
Regularity of Resolutions and Limits of Manifolds with a Uniform Contractibility Function
If a compact ANR is a Gromov-Hausdorff limit of closed n-manifolds with bounded contractibility functions, then it is an open cell-like image of each sufficiently close approximating manifold, resolving Moore's conjecture in this setting.