Morse-Bott functions on orthogonal groups

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BOZMA AYDIN H. I., Gillam W., ÖZTÜRK F.

Topology and its Applications, cilt.265, 2019 (SCI-Expanded, Scopus)

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 265
  • Basım Tarihi: 2019
  • Doi Numarası: 10.1016/j.topol.2019.07.001
  • Dergi Adı: Topology and its Applications
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Anahtar Kelimeler: Morse-Bott inequalities, Morse-Bott theory, Orthogonal groups, Perfect fillings of tables
  • Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
  • Boğaziçi Üniversitesi Adresli: Evet

Özet

We make a detailed study of various (quadratic and linear) Morse-Bott trace functions on the orthogonal groups O(n). We describe the critical loci of the quadratic trace function Tr(AXBXT) and determine their indices via perfect fillings of tables. We review the basic notions of Morse-Bott cohomology in a simple case where the set of critical points has two connected components. We then use these results to give a new Morse-theoretic computation of the mod 2 Betti numbers of SO(n).