Things move slowly in the KM-publishing world,
esp. compared with our pretty immediate forum
connection. There are observations/corrections/etc.
to be made to recent (& less recent) KMs yet not
seeing the light of day. ?!
So,
I’m coming to a quick connection for full display & reference
–ici!
(-;
I’m surprised that these corrections didn’t emerge in KM#168
–say, vice some cartoons & a curious splice note from one “John Shaw”
(who we should know to be GB).
And now still missing w/KM#169, though another “John Shaw”
note about (his own, but openly as GB) an “enchantment” !
The errors esp. and other contributing points should be
on our IGKT record in KM.
FYI, here’s information regarding Rob’s Fig.5 “mutant” knots
Conway & K-T --each of which adorns one of opposite gates
to the Isaac Newton Institute building ::
| The medallions in these gates, created by John Robinson,
| depict the only two knots with at most eleven crossings having
| the same (trivial) Alexander polynomial as the unknot.
| The North gate shows the knot studied by S Kinoshita and H Terasaka,
| while the South gate shows the knot discovered by JH Conway in his
| classification of eleven-crossing knots.
| Related as they are by Conway mutation, this pair of knots cannot be
| distinguished by any skein invariant. That they are topologically distinct
| can be proved by investigating representations of knot groups into finite
| matrix groups, by determination of knot genus, or by use of certain quantum invariants.
–dl*
Here they are again, still valid. (At least Hotmail assures
me that though replied-to msg. can’t be shown on compose
–for whatever reason-- it will be included.
–dl*
**From: Dan Lehman dan_lehman@hotmail.com
Sent: Tuesday, July 8, 2025 5:09 AM
Subject: Various KM corrections/information
I’m reminded that there are several past points
to set straight --after waiting to see if anybody else was
reading and minding them.
(km162:17-8 was caught by yChan, yea!, as #1425;
it had made an earlier appearance in KM and was
not ID’d by Rob Chisnall (!!), much to my surprise.
yChan is indulging in e2e Joints, so we should expect
him to look closely. (#1425 is much underrated,
notably by Ashley.)
We have previously dealt with the “wind knot” issue,
I hope; and Ian’s stolen imagery has also come to light
(he sent to me another case of stolen images, clearly
from a different --slightly-- knot he’d presented).
–dl*
====
Richard Hopkins at km163:06 likens the Sokal Constrictor Knot presented
by Jiri Brany at km162:12 to something presented by our French friends.
But this was anticipated a decade ago at km123:37-9 by Barry Mault’s
presentation of a “Gleipnir” floating binder that I designed so to give
greater & immediate tension to the nipping turn(s). This was discussed
on the IGKT forum in August 2009.
(The initial version, presented to the IGKT forum by Andrew Dahm,
had the tightening of the nipping turn(s) come only after the hauled-upon
ends had run nearly 360 degrees around the bound item(s); so I sought
a structure that tightened them immediately --as does Jiri’s.)
Also in KM#163, at p.11 Binh suggests that he has a “new knot”
for which have this URLink : https://bit.ly/KM163-7. That ends
Joint however appears in Harry Asher’s *A New System of Knotting,
Vol. 1, #20, which he names “Square Rigger”. This knot can be
improved by having the Tails embrace each other on their tuck out.
And the tangle makes for some good Eye Knots.
Dave Perry at km164:07 asks about an interlocked-loops Eye Knot
that he has discovered and has used for many years. It’s simply
a sort of “doubling” of what was presented as the Bollard Loop
at km083:33-7, further discussed at km085:45-6. Hensel & Gretel
in their heap of nonsense (EKFR) possibly --guessing at loading,
which they mostly never give-- show this on Plate 339 #4; and
there are non-doubled like structures given pl.28#94/5 & pl.32#145.
The doubling shown by Dave has benefits of greater security and
strength (I surmise --3 diameters to crush around vs. just 2),
and removes the instability of versions with the wrapped &
tucked Tail going in the wrong direction.
And at km165:32, Rob Chisnall’s fig.5 two images have a bad
crossing. Starting at the top arc of each knot, move around
clockwise and the 2nd crossing reached should be reversed.
–dl*
====*