Statements (42)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
knot
finitely presented group |
| gptkbp:fundamentalGroupOf |
complement of the figure-eight knot
|
| gptkbp:hasProperty |
linear
non-abelian residually finite torsion-free non-solvable Hopfian co-Hopfian word-hyperbolic can be realized as a Kleinian group first knot group known to be word-hyperbolic has abelianization Z × Z has deficiency 1 has non-trivial representation into GL(2, C) has non-trivial representation into GL(2, F_p) has non-trivial representation into GL(2, Q) has non-trivial representation into GL(2, R) has non-trivial representation into GL(2, Z) has non-trivial representation into PSL(2, C) has non-trivial representation into PSL(2, F_p) has non-trivial representation into PSL(2, Q) has non-trivial representation into PSL(2, R) has non-trivial representation into PSL(2, Z) has non-trivial representation into SL(2, C) has non-trivial representation into SL(2, F_p) has non-trivial representation into SL(2, Q) has non-trivial representation into SL(2, R) has non-trivial representation into SL(2, Z) has non-trivial representation into SU(1,1) has non-trivial representation into SU(2) has rank 2 non-elementary |
| gptkbp:hasSubgroup |
gptkb:PSL(2,_C)
|
| https://www.w3.org/2000/01/rdf-schema#label |
figure-eight knot group
|
| gptkbp:isomorphicTo |
free product of Z/2Z and Z/3Z
|
| gptkbp:presentedBy |
⟨ a, b | aba^{-1}b^{-1}ab^{-1}a^{-1}b = 1 ⟩
|
| gptkbp:relatedTo |
figure-eight knot
hyperbolic 3-manifolds |
| gptkbp:bfsParent |
gptkb:fundamental_group_of_knot_complement
|
| gptkbp:bfsLayer |
7
|