-
mathematical theory of knots, the
unknot, not knot, or
trivial knot, is the
least knotted of all knots. Intuitively, the
unknot is a
closed loop of rope without...
- are
joined so it
cannot be undone, the
simplest knot
being a ring (or "
unknot"). In
mathematical language, a knot is an
embedding of a
circle in 3-dimensional...
-
distinguishes the
trefoil from the
unknot. The
simplest such
invariant is tricolorability: the
trefoil is tricolorable, but the
unknot is not. In addition, virtually...
-
polynomial is
characterized by
taking the
value 1 on any
diagram of the
unknot and
satisfies the
following skein relation: ( t 1 / 2 − t − 1 / 2 ) V (...
- as well. The
standard Möbius
strip has the
unknot for a
boundary but is not a
Seifert surface for the
unknot because it is not orientable. The "checkerboard"...
-
property of
having the same
Alexander polynomial and
Conway polynomial as the
unknot. The
issue of the
sliceness of the
Conway knot was
resolved in 2020 by Lisa...
- mathematics, a
stuck unknot is a
closed polygonal chain in three-dimensional
space (a skew polygon) that is
topologically equal to the
unknot but
cannot be deformed...
- it the knot with the third-smallest
possible crossing number,
after the
unknot and the
trefoil knot. The figure-eight knot is a
prime knot. The name is...
- t ) = 1 {\displaystyle {\begin{aligned}P_{n}(
unknot)&=q^{n-1}+q^{n-3}+\cdots +q^{1-n}&&n>0\\P_{0}(
unknot)&=1\end{aligned}}} For n > 1 {\displaystyle n>1}...
- of
components is gcd(p, q)). A
torus knot is
trivial (equivalent to the
unknot) if and only if
either p or q is
equal to 1 or −1. The
simplest nontrivial...
