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AIMS Mathematics

2020, Volume 5, Issue 6: 7562-7581. doi: 10.3934/math.2020484
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Research article

On Reidemeister torsion of flag manifolds of compact semisimple Lie groups

  • 1.
    Department of Mathematics, King Abdulaziz University, 21589 Jeddah, Makkah, Saudi Arabia
  • 2.
    Department of Mathematics, AIBU Izzet Baysal University, Bolu, Turkey
  • 3.
    Department of Mathematics, Hacettepe University, Ankara, Turkey
  • 4.
    Department of Mathematics, Daejin University, Kyunggi 11159, Korea
  • 5.
    Research Institute for Natural Sciences, Hanyang University, Seoul 04763, Korea
  • Received: 25 June 2020 Accepted: 23 September 2020 Published: 24 September 2020

  • MSC : 57Q10, 16Z05, 14M15, 14N15, 22E67

  • In this paper we calculate Reidemeister torsion of flag manifold $K/T$ of compact semi-simple Lie group $K = SU_{n+1}$ using Reidemeister torsion formula and Schubert calculus, where $T$ is maximal torus of $K$. We find that this number is 1. Also we explicitly calculate ring structure of integral cohomology algebra of flag manifold $K/T$ of compact semi-simple Lie group $K = SU_{n+1 }$ using root data, and Groebner basis techniques.

    Citation: Cenap Özel, Habib Basbaydar, Yasar Sñzen, Erol Yilmaz, Jung Rye Lee, Choonkil Park. On Reidemeister torsion of flag manifolds of compact semisimple Lie groups[J]. AIMS Mathematics, 2020, 5(6): 7562-7581. doi: 10.3934/math.2020484

    Related Papers:

  • In this paper we calculate Reidemeister torsion of flag manifold $K/T$ of compact semi-simple Lie group $K = SU_{n+1}$ using Reidemeister torsion formula and Schubert calculus, where $T$ is maximal torus of $K$. We find that this number is 1. Also we explicitly calculate ring structure of integral cohomology algebra of flag manifold $K/T$ of compact semi-simple Lie group $K = SU_{n+1 }$ using root data, and Groebner basis techniques.


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  • © 2020 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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