Dual submanifolds in rational homology spheres
Fuquan Fang

TL;DR
This paper characterizes the possible dimensions and codimensions of dual submanifolds in simply connected rational homology spheres, providing a complete classification of such triples.
Contribution
It offers a comprehensive classification of integral triples describing dual submanifolds in rational homology spheres, resolving a fundamental geometric problem.
Findings
Complete characterization of admissible triples (n; m_+, m_-)
Identification of conditions for dual submanifold existence
Clarification of the topological structure of rational homology spheres
Abstract
Let be a simply connected rational homology sphere. A pair of disjoint closed submanifolds in are called dual to each other if the complement strongly homotopy retracts onto or vice-versa. In this paper we will give a complete answer of which integral triples can appear, where , and .
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
