Nitu just told me that the Toda and Mimura's "Topology of Lie Groups I and II" has everything I could ever want to know, so that's exciting.

Yeah that's true. Hard to find stuff though

I got a pdf, in case you want it.

Not to mention they don't seem to cover homology.

yeah, no dice.

Pontrjagin or Pontryagin?

The later

Wow, he was blind from the age of 14

Whoa.

Did you know Lefschetz had no hands?

And he lost both his hands before he became a mathematician.

I did not. Crazy

Does BG take a natural map G-->BG?

I guess just that bottom level of the bar construction.

Hm. No. wtf.

whoa @EricPeterson look at Peter May's second answer to this MO question: mathoverflow.net/questions/100910/…

holy shit I think I'm getting somewhere with all this nonsense.

along the forgetful map $BSp\to BU$, the generators in mod 2 homology $y_{4k}$ just go to $\pm(x_{2k})^2$! What luck!

good peter

lol

@JonBeardsley here are some thoughts: start with BSp(1). it has maps BU(1) --> BSp(1) and BSp(1) --> BU(2) given by symplectification and desymplectification. picking a coordinate H^* BU(1) = Z[[x]], a coordinate on H^* BSp(1) can be given as x * [-1]_G(x), corresponding under the forgetful map to the inclusion of the divisors of the form (a, -_G a) inside of BU(2)_H = Div_2^+ G

Hm.

just like BU_H is Div BU(1)_H, the same argument shows BSp_H is Div BSp(1)_H, and the maps BU --> BSp --> BSU of infinite lie groups are induced by pushing around by the maps in the previous line

what is your notation BU_H?

homology?

the formal scheme associated to H_* BU. i'm going to try not to give (m)any element-wise formulas, but when you find them, they should smell like these descriptions

Aha, I see.

not to nitpick, but you wrote BSU. I happen to be interested in going down to BSO, does it make a difference?

yes

I thought so, lol.

Hrmmmm. Well, at the moment I feel like I'm somewhat close just with this classical stuff.

And I guess I'd like to avoid talking about divisors and formal schemes, unless I have to, since ultimately I'm just trying to compute a Tor.

In other words, I've got elementwise formulas for $H_\ast(U,\mathbb{Z}/2)\to H_\ast(SO,\mathbb{Z}/2)$, and just need to figure out how to lift them to maps on classifying spaces.

BO(1)_H is like the 2-torsion in BU(1)_H; BO_H like the divisors on the 2-torsion; and BSO_H like the divisors on the 2-torsion which sum to zero, so in all i think you get a map which sends a divisor you've agreed to think of as (a, -a) to 2(a) if 2_G(a) = 0 and to 0 otherwise

maybe not very useful, but that's what i have to offer

Hmmmmm.

Interesting.

Okay. Yeah, that's weird. I mean, I've never really thought about these things in terms of divisors...

Thankyou btw :-)

hm, yeah, sure

i'm worried i've failed to properly describe H_* BO, but the rest of it is probably ok

w/e, someday these things will be written down and then we will really know

Haha, Yeah. I mean, maybe Strickland has written these things down?

Callan has informed that there are a lot of unpublished notes secreted about Neil's office.

he's done his best, but they're quite incomplete

Or at least, he's sort of, implied it. I won't say he's said it outright, but I've extrapolated.

Hrmph. Cartan calls this map $X\to BX$ the suspension. But it's not... not really.

(presumably the adjoint of the suspension map coming from the fact that $X\simeq \Omega BX$ or something...?)

the suspension map should be a map Sigma X --> BX, the inclusion of the 1-skeleton of the simplicial model of BX

i should leave the office, this is ridiculous

haha, i'm in the office too

You guys....you're making me feel bad

Remember Drew, it's not about who works the hardest, but who gets the most done.

And at the moment I'm spending an inordinate amount of time on something pretty dopey.

=P

And I'm working on everything but my thesis

ugh. i feel bad but i'm just going to ask this on MO. it might kind of a be dumb question, but i feel certain someone with way more experience than I in this stuff knows the answer.

endless secret neil documents mathoverflow.net/a/57161/1094

Hi guys

do you remember the argument showing that the category of chain complexes over a ring with the projective or injective model structure is not simplicial?

I think I knew it at some point, but forgot it

@FernandoMuro since you can recover the Dold-Kan correspondence from the "standard simplices" in chain complexes, my recollection is that this boils down to non-strict monoidal properties of the normalized chain functor

Whoa. there are a lot of people in this room who aren't talking.

I guess this is the cool spot to lurk these days.

lol

I'm just here not to miss on any interesting Morava stories

Hahah. Oh great. We really should change the name of this room.

Ha!

room topic changed to Jack Morava Fan Club: A room for anyone interested in homotopy theory, or any nearby fields (e.g. category theory, algebraic geometry). To activate chatjax in this room go to meta.math.stackexchange.com/questions/1088/… [homotopy-theory]

There you go.

I'll leave it up until Eric notices. I suspect he can change it back.

:-)

I was googling Mahowald today and came across this course of Paul Goerss: northwestern.edu/class-descriptions/4520/WCAS/MATH/105-6/…

I was somewhat surprised about the sort of Math courses offered in northwestern ;-)

actually, at first I thought the title od the course was a joke

lol

@JonBeardsley Well @JonBeardsley it is somehow the only non idle room; no need for coolness to attract a crowd when you are the only place in town ;-)

Well, one could certainly argue that it's the only place in town b/c of its coolness. =P

I did not claim it was not cool. Only that it were not necessary. :-)

Fair enough, lol.

Anyway, hopefully this room will stay dedicated to homotopy theory, even though it's the hot spot for lurkers.

room topic changed to Homotopy Theory: A room for anyone interested in homotopy theory, or any nearby fields (e.g. category theory, algebraic geometry). To activate chatjax in this room go to meta.math.stackexchange.com/questions/1088/… [homotopy-theory]

whoa! so the map of cobordism rings $\Omega^{SO}\to\Omega^O$ comes algebraically from reducing mod 2!

that is, there's an exact sequence of rings $\Omega^{SO}\overset{2}\to\Omega^{SO}\to \Omega^{O}$

but everyone probably already knew that, lol. wild.

the new os x is way more intelligent about multiple monitors