Manifolds with non-zero degree maps to nilmanifolds have controlled finite group actions, and a new iterated symmetry invariant forces rational cohomology rigidity over two-step nilmanifolds.
Diffeomorphism Groups of Compact 4-manifolds are not always Jordan
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
We show that if $M$ is a compact smooth manifold diffeomorphic to the total space of an orientable $S^2$ bundle over the torus $T^2$, then its diffeomorphism group does not have the Jordan property, i.e., Diff$(M)$ contains a finite subgroup $G_n$ for any natural number $n$ such that every abelian subgroup of $G_n$ has index at leat $n$. This gives a counterexample to an old conjecture of Ghys.
fields
math.GT 1years
2025 1verdicts
CONDITIONAL 1representative citing papers
citing papers explorer
-
Large and iterated finite group actions on manifolds admitting non-zero degree maps to nilmanifolds
Manifolds with non-zero degree maps to nilmanifolds have controlled finite group actions, and a new iterated symmetry invariant forces rational cohomology rigidity over two-step nilmanifolds.