H-spaces with Finiteness Conditions

L-S category of quaternionic Stiefel manifolds

“…It is known that the above exact sequence satisfies that if i(a) = x and i(b) = y then λ(x × y) = ab (see [5]). Now let us consider the projective plane of ΩX n,n−k .…”

Characterization of the Mod 3 Cohomology of the Compact, Connected, Simple, Exceptional Lie Groups of Rank 6

“…According to Stasheff [23], we have a spectral sequence {E r } converging to H * (P 3X ), where the E 1 -term is given by E p,q 1 = (⊗ p IH * (X)) q ∼ = H q (X ∧ p ) for p 6 3 and E p,q 1 = 0 for p > 4 with the differentials d 1,q 1 = −φ and d 2,q 1 = −φ ⊗ 1 + 1 ⊗φ. Since H q (X ∧ 4 ) = 0 for q 6 23, we have 10 , v 12 , v 16 , v 18 , v 24 ] as an algebra for q 6 23, where…”

“…Recall the following diagram (see [8] and [18]), where λ 1 is the suspension isomorphism, deg α j = −j, deg λ j = j, i j is induced from the inclusion, the two triangles are exact, α 1 • λ 1 = −φ, and α 2 • λ 2 = −φ ⊗ 1 + 1 ⊗φ (see [8]). …”

Torsion in the cohomology of finite loop spaces and the Eilenberg–Moore spectral sequence

“…It is a conjecture of Lin that for odd primes p every connected, 1-connected F pfinite H-space has this simple structure of indecomposable elements [15]. In the case of compact Lie groups this conjecture is true if p is odd and for p = 2 the only exceptions are the compact Lie groups Spin(n) for n ≥ 15 and E 8 [10].…”