Quadratic maps and Bockstein closed group extensions

Bockstein Closed 2-Group Extensions and Cohomology of Quadratic Maps

A central extension of the form E : 0 → V → G → W → 0, where V and W are elementary abelian 2-groups, is called Bockstein closed if the components qi ∈ H ∗(W,F2) of the extension class of E generate an ideal which is closed under the Bockstein operator. In this paper, we study the cohomology ring of G when E is a Bockstein closed 2-power exact extension. The mod-2 cohomology ring of G has a sim...

Bockstein Closed Central Extensions of Elementary Abelian 2-Groups I: Binding Operators

Let E be a central extension of the form 0 → V → G → W → 0 where V and W are elementary abelian 2-groups. Associated to E there is a quadratic map Q : W → V given by the 2-power map which uniquely determines the extension. This quadratic map also determines the extension class q of the extension in H(W,V ) and an ideal I(q) in H(G,Z/2) which is generated by the components of q. We say E is Bock...

Group Extensions of Gibbs-markov Maps

Supersimplicity and quadratic extensions

Elliptic curves over a supersimple field with exactly one extension of degree 2 have s-generic rational points.

Cannon–thurston Maps for Hyperbolic Free Group Extensions

This paper gives a detailed analysis of the Cannon–Thurston maps associated to a general class of hyperbolic free group extensions. Let F denote a free groups of finite rank at least 3 and consider a convex cocompact subgroup Γ ≤ Out(F), i.e. one for which the orbit map from Γ into the free factor complex of F is a quasi-isometric embedding. The subgroup Γ determines an extension EΓ of F, and t...