discussion with baez today... "splitting principle" ... sa weak pullback of stacks / weak pushout of theorys ... putting a flag on particular object in the theory...

sa... whether 1) "structure augmentation" here gives an embedding on "k-theory", or something like that... but also, whether 2) the given object splits in k-theory under the augmentation... sa taking the augmentation to be a flag ct a splitting... taking "k-theory" to be direct sum k-theory ct exact sequence k-theory ... sa which of 1), 2) fails in these 4 cases... or something like that...

??sa theory of lambda rings as "structure theory of k-theory classifying space/spectrum" in some sense??

??baez suggested sa "tall-wraith monoid" here...

sa "multiplicative characteristic class" as map (of spectrums or of spaces os) from classifying space for vector bundles to eilenberg-maclane spectrum of some commutative ring, taking direct sum of vector bundles to multiplication, in some sense...

??sa multiplicative characteristic class as determined by values on line bundles... sa splitting principle... sa using "splitting principle" (os...) to get multiplicative characteristic class from formal power series in x... sa splitting vector bundle into line bundles and then... ??? ... sa "formal power series in first chern class" ... ??sa "first chern class as "_only_" characteristic
class for line bundles...

??sa "cohomology of cp^infinity as close to formal power serieses" ... os...

??sa "symmetric function, suppressing mention of variables because it's symmetric in them..."
os... ??....

??sa "chern-weil" ... invariant polynomials... [classifying space for 1d vector bundles]^n -> classifying space for nd vector bundles ... sa strict equalizer of weyl group action at cohomology level ... os, asf os... sa case of general simple lie gp, os... asf os...

...didn't get around to discussing galois theory aspects (??sa "adams operations" asf...) today...