Finite Mod Research Articles

Deconstructing Hopf spaces

We characterize Hopf spaces with finitely generated cohomology as an algebra over the Steenrod algebra. We “deconstruct” the original space into an H-space Y with finite mod p cohomology and a finite number of p-torsion Eilenberg-Mac Lane spaces. We give a precise description of homotopy commutative H-spaces in this setting.

Homotopy exponents of Harper’s spaces

For an odd prime $p$, we show that the $p$-primary homotopy exponent of Harper’s rank 2 finite mod-$p$ $H$-space $K_{p}$ is $p^{p^{2}+p}$. We then use this to show that the 3-primary homotopy exponent of each of the exceptional Lie groups $F_{4}$ and $E_{6}$ is $3^{12}$.

Non-simply connected H-spaces with finiteness conditions

This article is concerned with homotopy properties of H-spaces X that are reflected in the module of indecomposables QH*(X; [ ]p). It is shown that mod p H-spaces X of finite type with finite transcendence degree mod p cohomology and locally finite QH*(X; [ ]p) are Bℤ/p-null spaces, Eilenberg–MacLane spaces K(ℤˆp, 2), K(ℤ/pr, 1), and extensions of those. If we restrict attention to H-spaces with noetherian mod p cohomology algebra, then we are left with finite mod p H-spaces and Eilenberg–MacLane spaces.

H-SPACES WITH NOETHERIAN MOD TWO COHOMOLOGY ALGEBRA

The object of this paper is to analyse the structure of connected H-spaces with noetherian mod two cohomology algebra. We will show that, up to 2-completion, they are, essentially, finite mod 2 H-spaces and their 3-connected covers, CP ∞ , B Z/2 r and certain extensions of these.

Homotopy commutativity, homotopy associativity and power spaces

A finite mod 3 homotopy commutative, homotopy associative simply connected H-space has mod 3 cohomology isomorphic to the cohomology of a product of Sp(2)s. This result generalizes to other odd primes.