The First and Second Homotopy Groups of a Homogeneous Space of a Complex Linear Algebraic Group

Mikhail Borovoi*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

Let X be a homogeneous space of a connected linear algebraic group G defined over the field of complex numbers C. Let x ∈ X(C) be a point. We denote by H the stabilizer of x in G. When H is connected, we compute the topological fundamental group π1top(X(C),x). Moreover, we compute the second homotopy group π2top(X(C),x).

Original languageEnglish
Pages (from-to)687-700
Number of pages14
JournalJournal of Lie Theory
Volume33
Issue number2
StatePublished - 2023

Funding

FundersFunder number
Israel Science Foundation1030/22

    Keywords

    • Fundamental group
    • homogeneous space
    • linear algebraic group
    • second homotopy group

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