The first and second homotopy groups of a homogeneous space of a complex linear algebraic group

2022/07/18 by Borovoi, Mikhail
#14F35 #14M17 #20G20 #Algebraic Geometry (math.AG) #Algebraic Topology (math.AT) #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2207.08887

Abstract

Let X be a homogeneous space of a connected linear algebraic group G defined over the field of complex numbers \mathbb C. Let x∈ X(\mathbb C) be a point. We denote by H the stabilizer of x in G. When H is connected, we compute the topological fundamental group π₁^{\rm top}(X(\mathbb C),x). Moreover, we compute the second homotopy group π₂^{\rm top}(X(\mathbb C),x).

Related

• Le groupe fondamental d'un espace homogène d'un groupe algébrique linéaire
• Étale homotopy groups of algebraic groups and homogeneous spaces
• On the second lower quotient of the fundamental group
• Topological rigidity of SL₂-quotients
• On H-groups and their applications to topological homotopy groups