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## Roots of Unity Associated to Strongly Detected Boundary Slopes

Citations: | 5 - 0 self |

### Citations

266 |
Varieties of group representations and splittings of 3-manifolds,
- Culler, Shalen
- 1983
(Show Context)
Citation Context ... irreducible algebraic curve in X(M) and let ˜ X0 be the smooth projective completion of X0. Note that each trace function τγ extends to a rational function ˜τγ on ˜ X0. By the fundamental theorem of =-=[4]-=-, if x ∈ ˜ X0 is a pole of some trace function ˜τγ, then there is an essential surface S in M associated to x via an action of π1(M) on a Bass–Serre simplicial tree. (Note that the set of poles of all... |

154 | curves associated to character varieties of 3-manifolds, Invent
- Cooper, Culler, et al.
- 1994
(Show Context)
Citation Context ... the ideal point x of ˜ X0. Moreover, the trace function of the primitive element β ∈ π1(∂M) (or its inverse) corresponding to the ∂-slope of S has finite value at the ideal point x. It was proved in =-=[1]-=- that ˜τβ(x) =λ + λ−1 for some root of unity λ. The order of λ has geometric significance; it divides the number of boundary 16231624 S. Kuppum & X. Zhang K 1 1 1 K 2 2 2 2 (a) (b) Fig. 1. The Whiteh... |

42 | Remarks on the A-polynomial of a knot - Cooper, Long - 1996 |

32 |
Incompressible surfaces in punctured-torus bundles
- Floyd, Hatcher
- 1982
(Show Context)
Citation Context ...(see [7, Proposition 3], note that the slopes given in [7] differ from ours by sign). So Mn is hyperbolic for each n>4. Incompressible surfaces in hyperbolic punctured torus bundles are classified in =-=[6, 3]-=-. According to the algorithm given in [6], M4k+2 has two boundary slopes, 4 and 1/k, besides the boundary slope 0 of a fiber (note that Mn has the LR-decomposition −RLn−4 , and that the slopes given i... |

24 |
Ideal points and incompressible surfaces in two-bridge knot complements
- Ohtsuki
- 1994
(Show Context)
Citation Context ...es of roots of unity associated to strongly detected boundary slopes are ±1. For instance, this is always the case for the exterior of any 2-bridge knot in S 3 (this result is implicitly contained in =-=[8]-=-). In [5], several examples of roots of unity of order four and six were given. The main purpose of this paper is to produce an infinite family of knot manifolds each of which has a root of unity of o... |

20 |
Incompressible surfaces in once-punctured torus bundles
- Culler, Jaco, et al.
(Show Context)
Citation Context ...(see [7, Proposition 3], note that the slopes given in [7] differ from ours by sign). So Mn is hyperbolic for each n>4. Incompressible surfaces in hyperbolic punctured torus bundles are classified in =-=[6, 3]-=-. According to the algorithm given in [6], M4k+2 has two boundary slopes, 4 and 1/k, besides the boundary slope 0 of a fiber (note that Mn has the LR-decomposition −RLn−4 , and that the slopes given i... |

16 |
Surgeries on the Whitehead link yield geometrically similar manifolds, Topology ’90
- Hodgson, Meyerhoff, et al.
- 1990
(Show Context)
Citation Context ...hose edge polynomial has a root of unity of order 4, for each k>0. Note that each Mn is a punctured torus bundle with monodromy ( −n +2 1 −1 0 ) (see [7, Proposition 3], note that the slopes given in =-=[7]-=- differ from ours by sign). So Mn is hyperbolic for each n>4. Incompressible surfaces in hyperbolic punctured torus bundles are classified in [6, 3]. According to the algorithm given in [6], M4k+2 has... |

13 | Examples of non-trivial roots of unity at ideal points of hyperbolic 3-manifolds
- Dunfield
- 1999
(Show Context)
Citation Context ...ts of unity associated to strongly detected boundary slopes are ±1. For instance, this is always the case for the exterior of any 2-bridge knot in S 3 (this result is implicitly contained in [8]). In =-=[5]-=-, several examples of roots of unity of order four and six were given. The main purpose of this paper is to produce an infinite family of knot manifolds each of which has a root of unity of order four... |