Real homogeneous spaces, Galois cohomology, and Reeder puzzles

Mikhail Borovoi, Zachi Evenor

Research output: Contribution to journalArticlepeer-review


Let G be a simply connected absolutely simple algebraic group defined over the field of real numbers R. Let H be a simply connected semisimple R-subgroup of G. We consider the homogeneous space X=G/H. We ask: how many connected components has X(R)? We give a method of answering this question. Our method is based on our solutions of generalized Reeder puzzles.

Original languageEnglish
Pages (from-to)307-365
Number of pages59
JournalJournal of Algebra
StatePublished - 1 Dec 2016


  • Labelings of a Dynkin diagram
  • Real Galois cohomology
  • Real homogeneous space
  • Reeder puzzle
  • Simply connected real group


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