Poetic Summary of Results

(of "A multiplicative comparison...")

Segal and Waldhausen
Both have built K-theories
These are the same viewed with
Additive eyes.

Now we have proved that their
Multiplications are
Not multifarious:
What a surprise.

The (Optimistic) Spectral Sequence Song

(To the tune of "The Garden Song")

Inch by inch, row by row
Watch the spectral sequence grow
All the differentials show
The term at infinity

Page by page, prime by prime
Calculate them all in time
Put them together and we'll find
An answer over Z

The K-theory Song

(With apologies to Tigger)

Vectors make wonderful bundles
And bundles are wonderful things!
You can add an additive inverse
And turn them into a ring!

Their operations--like conjugation--
Are fun, fun, fun, fun, fun.
The most wonderful thing about bundles is
Hopf invariant one!