Only rational homology spheres admit $Ω(f)$ to be union of DE attractors

Details Only rational homology spheres admit $Ω(f)$ to be union of DE attractors Only rational homology spheres admit $Ω(f)$ to be union of DE attractors

2008-12-06

arxiv.org/abs/0812.1260v3

Mathematics

Geometric Topology

23 pages, 2 figures

Scientific paper

If there exists a diffeomorphism $f$ on a closed, orientable $n$-manifold $M$ such that the non-wandering set $\Omega(f)$ consists of finitely many orientable $(\pm)$ attractors derived from expanding maps, then $M$ must be a rational homology sphere; moreover all those attractors are of topological dimension $n-2$. Expanding maps are expanding on (co)homologies.

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