Dual submanifolds in rational homology spheres

Fuquan Fang

doi:10.1007/s11425-017-9130-9

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arXiv · 1701.00195

Dual submanifolds in rational homology spheres

Fuquan Fang

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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 $m_-={codim}M_- -1$.

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BibTeX RIS

Fuquan Fang. 2017-01-01. Dual submanifolds in rational homology spheres. https://doi.org/10.1007/s11425-017-9130-9

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