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Dual submanifolds in rational homology spheres
- Source :
- Science China Mathematics. 60:1549-1560
- Publication Year :
- 2017
- Publisher :
- Springer Science and Business Media LLC, 2017.
-
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 $m_-={codim}M_- -1$.
- Subjects :
- Mathematics - Differential Geometry
Complement (group theory)
Mathematics::Commutative Algebra
General Mathematics
Homotopy
010102 general mathematics
Sigma
Geometric Topology (math.GT)
Disjoint sets
Homology (mathematics)
01 natural sciences
Homology sphere
Combinatorics
Mathematics - Geometric Topology
Differential Geometry (math.DG)
0103 physical sciences
Simply connected space
FOS: Mathematics
Algebraic Topology (math.AT)
SPHERES
Mathematics - Algebraic Topology
010307 mathematical physics
0101 mathematics
Mathematics
Subjects
Details
- ISSN :
- 18691862 and 16747283
- Volume :
- 60
- Database :
- OpenAIRE
- Journal :
- Science China Mathematics
- Accession number :
- edsair.doi.dedup.....970ec505693d8dd63f5d152c62451a5b