TY - JOUR

T1 - The First and Second Homotopy Groups of a Homogeneous Space of a Complex Linear Algebraic Group

AU - Borovoi, Mikhail

N1 - Publisher Copyright:
© 2023 Heldermann Verlag.

PY - 2023

Y1 - 2023

N2 - 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).

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

UR - http://www.scopus.com/inward/record.url?scp=85169842517&partnerID=8YFLogxK

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AN - SCOPUS:85169842517

SN - 0949-5932

VL - 33

SP - 687

EP - 700

JO - Journal of Lie Theory

JF - Journal of Lie Theory

IS - 2

ER -