The unknot arises in the mathematical theory of knots. Intuitively, the unknot is a closed loop of rope without a knot in it. A knot theorist would describe the unknot as an image of any embedding that can be deformed, i.e. ambient-isotoped, to the standard unknot, i.e. the embedding of the circle as a geometrically round circle. The unknot is also called the trivial knot. An unknot is the identity element with respect to the knot sum operation.
Deciding if a particular knot is the unknot was a major driving force behind knot invariants, since it was thought this approach would possibly give an efficient algorithm to recognize the unknot from some presentation such as a knot diagram. Currently there are several well-known unknot recognition algorithms (not using invariants), but they are either known to be inefficient or have no efficient implementation. It is not known whether many of the current invariants, such as finite type invariants, are a complete invariant of the unknot, but knot Floer homology is known to detect the unknot. Even if they were, the problem of computing them efficiently remains.
Lying awake in my bed
Thinking things you said
Everything that I do
Somehow leads me to you
(Closer to your love)
Lift my spirit so high
You're all I need to get by
I've been counting days
Forever thinking ways
(To get closer to your love)
This loneliness will end
The day you reappear, yeah
Living in this world without you here
It's like trying to reach the heavens
When I've got no wings to fly
You can make this feeling disappear
Come on over baby, come on over to me
Living in this world without you here
It's like trying to reach the heavens
When I've got no wings to fly
Only you can make this feeling disappear
Come on over baby, come on over to me, yeah
You started something in me
Stirring constantly
Though we're oceans apart
I build a bridge to your heart
(Closer to your love)
Like a bird on the wire
Sing my heart's desire
Caught in something so strong
I rarely feel I belong
(In the shelter of your love)
This loneliness will end
The day you reappear
Living in this world without you here
It's like trying to reach the heavens
When I've got no wings to fly
You can make this feeling disappear
Come on over baby, come on over to me
Living in this world without you here
It's like trying to reach the heavens
When I've got no wings to fly
Only you can make this feeling disappear
Come on over baby, come on over to me
I just can't keep it in
I've got to let you know
I got so much love to give you
Gonna let these feelings show, yeah, yeah
Living in this world without you here
It's like trying to reach the heavens
When I've got no wings to fly
You can make this feeling disappear
Come on over baby, come on over to me
Living in this world without you here
It's like trying to reach the heavens
When I've got no wings to fly
Only you can make this feeling disappear
Feeling's disappear
Come on over baby, come on in babe
Come on over to me, yeah
Living in this world without you here
(Living in this world without you here)
It's like trying to reach the heavens
When I've got no wings to fly
(Yeah)
You can make this feeling disappear
Come on over baby, come on over to me baby
Living in this world without you here
It's like trying to reach the heavens
When I've got no wings to fly
(Got no wings to fly)
Only you can make this feeling disappear
Come on over baby, come on over to me
Living in this world without you here
It's like trying to reach the heavens
When I've got no wings to fly
You can make this feeling disappear
Come on over baby, come on over to me
Living in this world without you here
It's like trying to reach the heavens
When I've got no wings to fly
Only you can make this feeling disappear