Cohomologie de BSpin(n). - Irma

2
BSpin(n)

n
G
G
G BG
BG
Sqk
H∗(BOn,Z2)H∗(BSOn,Z2)
H∗(BOn,Z2)
H∗(BSOn,Z2)
Spinn(R)

BSpin(n)BSpin(n)
p:E→B G E p
E/G B
20
2G
BG
4
3H∗(Gn(R∞))
Spin(n)
SO(n)

ξ
B
E
E(ξ)
π:E→B
∀b∈BR C
π−1(b)
b∈B
U⊂B b n ≥0h:
U×Rn→π−1(U)b∈U x 7→ h(b, x)
Rnπ−1(b)π−1(b)
b Fb(ξ)B
B(ξ)
•ξ
n ξ
•B
π:B×Rn→B
n
•
ξ η
E(ξ)E(η)
f:E(ξ)→E(η)f
Fb(ξ)Fb(η)
RPnn n ≥1
RPnRn+1 [u]u