Graphs and projective plaines in 3-manifolds
Proper homotopy equivalent compact P2-irreducible and sufficiently large 3-manifolds are homemorphic. The result is not known for irreducible 3-manifolds that contain 2-sided projective planes, even if one assumes the Poincaré conjecture. In this paper to such a 3-manifold M is associated a graph G(...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
1986-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171286000698 |
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| Summary: | Proper homotopy equivalent compact P2-irreducible and sufficiently large 3-manifolds are homemorphic. The result is not known for irreducible 3-manifolds that contain 2-sided projective planes, even if one assumes the Poincaré conjecture. In this paper to such a 3-manifold M is associated a graph G(M) that specifies how a maximal system of mutually disjoint non-isotopic projective planes is embedded in M, and it is shown that G(M) is an invariant of the homotopy type of M. On the other hand it is shown that any given graph can be realized as G(M) for infinitely many irreducible and boundary irreducible M. |
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| ISSN: | 0161-1712 1687-0425 |