Homeomorphisms of Quaternion space and projective planes in four space
| Autor: | T. M. Price |
|---|---|
| Rok vydání: | 1977 |
| Předmět: |
Pure mathematics
Collineation Projective unitary group TheoryofComputation_ANALYSISOFALGORITHMSANDPROBLEMCOMPLEXITY General Mathematics Complex projective space Mathematical analysis Projective space Projective plane Quaternionic projective space Real projective space Mathematics Projective geometry |
| Zdroj: | Journal of the Australian Mathematical Society. 23:112-128 |
| ISSN: | 1446-8107 1446-7887 |
| DOI: | 10.1017/s1446788700017407 |
| Popis: | It is known that all locally flat projective planes in S4 have homeomorphic normal disk bundles. In this paper we investigate the homeomorphisms of Q3 (= boundary of the normal disk bundle) on to itself. We show that a homeomorphisms of Q3 onto itself is determined, up to isotopy, by the outerautomorphism of π1(Q3) that it induces. Since Q3 is an irreducible, not sufficiently large 3-manifold with finite fundamental group this characterization is interesting in its own right. The characterization of homeomorphisms is then used to study certain questions about embeddings of the projective plane in S4. One result is that there are at most two distinct projective planes in S4 with a given complement. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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