Paper
Periodicity in the homology of moduli spaces of disconnected submanifolds
Authors
Nicolas Guès
Abstract
We show that the moduli space of suitably embedded copies of a closed smooth manifold inside a closed smooth manifold satisfies cohomological periodicity over when grows, with an explicit linear bound on the period and the periodicity range. This generalizes a known result about configuration spaces. We also show integral stability of the cohomology when is open, reproving a result of Palmer and improving the slope when inverting . The main input in the proof is Goodwillie and Klein's multiple disjunction lemma for embedding spaces. As a corollary we get stability and periodicity results for some classes of symmetric diffeomorphism groups of manifolds.