Back to Search
Start Over
Existence of Taut Foliations on Seifert Fibered Homology 3-spheres
- Source :
- Canadian Journal of Mathematics. 66:141-169
- Publication Year :
- 2014
- Publisher :
- Canadian Mathematical Society, 2014.
-
Abstract
- This paper concerns the problem of existence of taut foliations among 3-manifolds. Since the contribution of David Gabai, we know that closed 3-manifolds with non-trivial second homology group admit a taut foliations. The essential part of this paper focuses on Seifert fibered homology 3-spheres. The result is quite different if they are integral or rational but non-integral homology 3-spheres. Concerning integral homology 3-spheres, we prove that all but the 3-sphere and the Poincar\'e 3-sphere admit a taut foliation. Concerning non-integral homology 3-spheres, we prove there are infinitely many which admit a taut foliation, and infinitely many without taut foliation. Moreover, we show that the geometries do not determine the existence of taut foliations on non-integral Seifert fibered homology 3-spheres.<br />Comment: 34 pages, 1 figure
- Subjects :
- Pure mathematics
General Mathematics
Taut foliation
General Topology (math.GN)
Physics::Physics Education
Fibered knot
Geometric Topology (math.GT)
Homology (mathematics)
Mathematics::Geometric Topology
Mathematics - Geometric Topology
FOS: Mathematics
Mathematics::Differential Geometry
Mathematics::Symplectic Geometry
Mathematics - General Topology
Mathematics
Subjects
Details
- ISSN :
- 14964279 and 0008414X
- Volume :
- 66
- Database :
- OpenAIRE
- Journal :
- Canadian Journal of Mathematics
- Accession number :
- edsair.doi.dedup.....e589d9336fba56c8144770ad1ad4bfe8