Question

Is there an example of two topologically different knots with the exact same Conway notation?

score 80 · Answer 1 · 2026-03-26 21:35:02

80

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Is there an example of two topologically different knots with the exact same Conway notation?

Published on 26 Mar 2026 - 21:35

score 79 · Answer 2 · 2026-03-26 23:09:44

79

Views

What do variables $A$ and $t$ represent in the normalized bracket polynomial and jones polynomial respectively?

Published on 26 Mar 2026 - 23:09

score 139 · Answer 3 · 2026-03-30 03:20:23

139

Views

How many different planar embeddings of a graph are possible?

Published on 30 Mar 2026 - 3:20

score 362 · Answer 4 · 2026-03-26 21:34:52

362

Views

How can I proof: Figure-Eight Knot is 5-colorable?

Published on 26 Mar 2026 - 21:34

score 104 · Answer 5 · 2021-10-24 18:07:14

104

Views

Links to Étienne Ghys's 2006 ICM Talk "Knots and Dynamics"

Published on 24 Oct 2021 - 18:07

score 201 · Answer 6 · 2026-03-28 06:00:34

201

Views

If an embedding of $S^1\times I$ has nice edges, are the edges ambiently isotopic?

Published on 28 Mar 2026 - 6:00

score 54 · Answer 7 · 2026-03-26 21:26:22

54

Views

Definition of Vassiliev invariants for framed oriented knots

Published on 26 Mar 2026 - 21:26

score 157 · Answer 8 · 2026-03-28 05:59:26

157

Views

How to tell if a straight line will pass through a closed loop in 3-space?

Published on 28 Mar 2026 - 5:59

score 62 · Answer 9 · 2021-11-08 23:38:59

62

Views

(physics of an idealized string) Show that this expanding cylinder will unravel this loop

Published on 08 Nov 2021 - 23:38

score 46 · Answer 10 · 2026-03-26 21:35:27

46

Views

Singular framing of a singular knot

Published on 26 Mar 2026 - 21:35

score 103 · Answer 11 · 2026-03-25 12:27:09

103

Views

Apparent contradiction with gluing 2-handle to a 4-manifold all being isotopic.

Published on 25 Mar 2026 - 12:27

score 97 · Answer 12 · 2021-11-18 20:46:05

97

Views

Show that two framed links with same linking matrix are framed cobordant in $\mathbb{S}^3$

Published on 18 Nov 2021 - 20:46

score 279 · Answer 13 · 2026-03-26 21:25:24

279

Views

How to recognize torus knots

Published on 26 Mar 2026 - 21:25

score 133 · Answer 14 · 2026-03-26 23:09:41

133

Views

HOMFLY polynomial is invariant under Reidemeister moves

Published on 26 Mar 2026 - 23:09

score 154 · Answer 15 · 2021-11-29 23:05:09

How to know if a group is the fundamental group of a knot complement and if so how would you reconstruct the original knot from it?

List Question

Is there an example of two topologically different knots with the exact same Conway notation?

What do variables $A$ and $t$ represent in the normalized bracket polynomial and jones polynomial respectively?

How many different planar embeddings of a graph are possible?

How can I proof: Figure-Eight Knot is 5-colorable?

Links to Étienne Ghys's 2006 ICM Talk "Knots and Dynamics"

If an embedding of $S^1\times I$ has nice edges, are the edges ambiently isotopic?

Definition of Vassiliev invariants for framed oriented knots

How to tell if a straight line will pass through a closed loop in 3-space?

(physics of an idealized string) Show that this expanding cylinder will unravel this loop

Singular framing of a singular knot

Apparent contradiction with gluing 2-handle to a 4-manifold all being isotopic.

Show that two framed links with same linking matrix are framed cobordant in $\mathbb{S}^3$

How to recognize torus knots

HOMFLY polynomial is invariant under Reidemeister moves

How to know if a group is the fundamental group of a knot complement and if so how would you reconstruct the original knot from it?

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