The lattice of branched covers over the figure-eight knot
نویسندگان
چکیده
منابع مشابه
Injectively Immersed Tori in Branched Covers over the Figure Eight Knot
The importance of this result lies primarily in the fact [HLM] that the figure eight knot is universal. That is, that all closed, orientable 3-manifolds are obtainable as branched covers over S, branched over the knot. We also obtain results about incompressible (embedded) tori in some cases. Existence or nonexistence of injectively immersed tori is critical to the understanding of a 3-manifold...
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We obtain a branched spherical CR structure on the complement of the figure eight knot whose holonomy representation was given in [4]. There are essentially two boundary unipotent representations from the complement of the figure eight knot into PU(2, 1), we call them ρ1 and ρ2. We make explicit some fundamental differences between these two representations. For instance, seeing the figure eigh...
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In this paper, we compute the symplectic Floer homology of the figure eight knot. This provides first nontrivial knot with trivial symplectic Floer homology.
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In this paper, we introduce a sequence of invariants of a knot K in S3 : the knot Floer homology groups ĤFK(Σm(K); K̃, i) of the preimage of K in the m–fold cyclic branched cover over K . We exhibit ĤFK(Σm(K); K̃, i) as the categorification of a well-defined multiple of the Turaev torsion of Σm(K)− K̃ in the case where Σm(K) is a rational homology sphere. In addition, when K is a two-bridge knot, ...
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ژورنال
عنوان ژورنال: Topology and its Applications
سال: 1990
ISSN: 0166-8641
DOI: 10.1016/0166-8641(90)90080-l