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The Klein Four
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Calculating
I can't see the circles
When you map them into spheres：
If they are one-connected
Then pi-one disappears
So homotopy theory
Is the game for me
The n-holes that surround you
All look the same to me
So is this thing a doughnut
Or is it a coffee cup?
I just can't tell the difference
Until you fill it up
There's not much to examine
Just one Greek letter pi
But you really can't be serious
If you have to ask me why
I sit and cry
'Cause I am calculating
The stable groups of spheres
Don't know who I'm kidding
Imagining it's clear
The Adams spectral sequence
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A tool but a headache
I don't suppose it's worth the time,
It's worth the time, the time that I will take
Everyone keeps asking, what's it all about?
I used to be so certain, now I can't figure out
Complex cobordism, the alpha family
The J-homomorphism, what will its image be?
Just wait and see
(Chorus)
But I'm thinking it over anyway
I'm on the way that Adams shows
To get pi-star from pi-BO
But don't you say that I'll never know
'Cause that's just how dissertations go
They come oh so slow, oh...
(Chorus)
And maybe I'll have solved it
By this time next year
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