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

Mikhail Borovoi

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

Mikhail Borovoi^*

^*Corresponding author for this work

School of Mathematical Sciences

Research output: Contribution to journal › Article › peer-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 π₁^top(X(C),x). Moreover, we compute the second homotopy group π₂^top(X(C),x).

Original language	English
Pages (from-to)	687-700
Number of pages	14
Journal	Journal of Lie Theory
Volume	33
Issue number	2
State	Published - 2023

Keywords

Fundamental group
homogeneous space
linear algebraic group
second homotopy group

Cite this

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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).",

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AB - 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).

KW - Fundamental group

KW - homogeneous space

KW - linear algebraic group

KW - second homotopy group

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

Abstract

Keywords

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