Haken manifolds and representations of their fundamental groups in SL(2, C)

Motegi, Kimihiko

doi:10.1016/0166-8641(88)90019-3

Cited by 24 publications

(21 citation statements)

References 1 publication

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“…The converse of this is not true in general; i.e., a closed Haken manifold W may not have a positive dimensional SL 2 (C)-or PSL 2 (C)-character variety. Examples of such Haken manifolds have been described by K. Motegi in [33], obtained by gluing two torus knot exteriors according to a well-chosen gluing homeomorphism of their boundaries. Clearly none of Motegi's examples is hyperbolic.…”

Section: Corollary 13 ([17]mentioning

confidence: 99%

On Culler-Shalen Seminorms and Dehn Filling

Boyer¹,

Zhang²

1998

The Annals of Mathematics

114

239

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Section: Corollary 13 ([17]mentioning

confidence: 99%

On Culler-Shalen Seminorms and Dehn Filling

Boyer¹,

Zhang²

1998

The Annals of Mathematics

114

239

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“…The fundamental group of M 3 can be represented by π 1 (M 3 ). The nature of π 1 (M 3 ) is the type of SL(2, C), which is a homeomorphism of π 1 (M 3 ) to SL(2, C) [6]. It is important to note that the space of representation of fundamental group π 1 (M 3 ) in the SL(2, C) structure is a complex algebraic set [6].…”

Section: Topological Algebraic Sets and Manifoldsmentioning

confidence: 99%

Surjective Identifications of Convex Noetherian Separations in Topological (C, R) Space

Bagchi

2021

Symmetry

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The interplay of symmetry of algebraic structures in a space and the corresponding topological properties of the space provides interesting insights. This paper proposes the formation of a predicate evaluated P-separation of the subspace of a topological (C, R) space, where the P-separations form countable and finite number of connected components. The Noetherian P-separated subspaces within the respective components admit triangulated planar convexes. The vertices of triangulated planar convexes in the topological (C, R) space are not in the interior of the Noetherian P-separated open subspaces. However, the P-separation points are interior to the respective locally dense planar triangulated convexes. The Noetherian P-separated subspaces are surjectively identified in another topological (C, R) space maintaining the corresponding local homeomorphism. The surjective identification of two triangulated planar convexes generates a quasiloop–quasigroupoid hybrid algebraic variety. However, the prime order of the two surjectively identified triangulated convexes allows the formation of a cyclic group structure in a countable discrete set under bijection. The surjectively identified topological subspace containing the quasiloop–quasigroupoid hybrid admits linear translation operation, where the right-identity element of the quasiloop–quasigroupoid hybrid structure preserves the symmetry of distribution of other elements. Interestingly, the vertices of a triangulated planar convex form the oriented multiplicative group structures. The surjectively identified planar triangulated convexes in a locally homeomorphic subspace maintain path-connection, where the right-identity element of the quasiloop–quasigroupoid hybrid behaves as a point of separation. Surjectively identified topological subspaces admitting multiple triangulated planar convexes preserve an alternative form of topological chained intersection property.

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“…The construction of deformations of a representation used in this section is called a bending construction or simply a bending. See [11,17] as a reference. Here we compute X irr (Σ(K, K)) for the trefoil knot and the figure-eight knot K by using a presentation of a twist knot.…”

Section: Computational Observationmentioning

confidence: 99%