Dual submanifolds in rational homology spheres

Abstract

Let $\Sigma$ be a simply connected rational homology sphere. A pair of disjoint closed submanifolds $M_{+},M_{-}$ in $\Sigma$ are called dual to each other if the complement $\Sigma -M_{+}$ strongly homotopy retracts onto $M_{-}$ or vice-versa. In this paper we will give a complete answer of which integral triples $(n;m_{+},m_{-})$ can appear, where $n=dim\Sigma -1$, $m_{+}=codim{M}_{+}-1$ and $m_{-}=codim{M}_{-}-1$.

References in corpus (1)

• Isoparametric foliations, diffeomorphism groups and exotic smooth structures

Cited by in corpus (1)

• Topology and curvature of isoparametric families in spheres