On reidemeister torsion of flag manifolds of compact semisimple lie groups

Cenap Özel; Habib Basbaydar; Yasar Sözen; Erol Yilmaz; Jung Rye Lee; Choonkil Park

doi:10.3934/math.2020484

On reidemeister torsion of flag manifolds of compact semisimple lie groups

Cenap Özel
, Habib Basbaydar
, Yasar Sözen
, Erol Yilmaz
, Jung Rye Lee
, Choonkil Park

Division of Topology

King Abdulaziz University
Abant Izzet Baysal University
Daejin University
Hanyang University

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper we calculate Reidemeister torsion of flag manifold K/T of compact semisimple Lie group K = S U_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 = S U_n+1 using root data, and Groebner basis techniques.

Original language	English
Pages (from-to)	7562-7581
Number of pages	20
Journal	AIMS Mathematics
Volume	5
Issue number	6
DOIs	https://doi.org/10.3934/math.2020484
Publication status	Published - 2020

Keywords

Flag manifolds
Graded inverse lexicographic order
Groebner-Shirshov bases
Reidemeister torsion
Schubert calculus
Weyl groups

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10.3934/math.2020484

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title = "On reidemeister torsion of flag manifolds of compact semisimple lie groups",

abstract = "In this paper we calculate Reidemeister torsion of flag manifold K/T of compact semisimple Lie group K = S Un+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 = S Un+1 using root data, and Groebner basis techniques.",

keywords = "Flag manifolds, Graded inverse lexicographic order, Groebner-Shirshov bases, Reidemeister torsion, Schubert calculus, Weyl groups",

author = "Cenap {\"O}zel and Habib Basbaydar and Yasar S{\"o}zen and Erol Yilmaz and Lee, \{Jung Rye\} and Choonkil Park",

note = "Publisher Copyright: {\textcopyright} 2020 the Author(s), licensee AIMS Press.",

year = "2020",

doi = "10.3934/math.2020484",

language = "English",

volume = "5",

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T1 - On reidemeister torsion of flag manifolds of compact semisimple lie groups

AU - Özel, Cenap

AU - Basbaydar, Habib

AU - Sözen, Yasar

AU - Yilmaz, Erol

AU - Lee, Jung Rye

AU - Park, Choonkil

PY - 2020

Y1 - 2020

N2 - In this paper we calculate Reidemeister torsion of flag manifold K/T of compact semisimple Lie group K = S Un+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 = S Un+1 using root data, and Groebner basis techniques.

AB - In this paper we calculate Reidemeister torsion of flag manifold K/T of compact semisimple Lie group K = S Un+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 = S Un+1 using root data, and Groebner basis techniques.

KW - Flag manifolds

KW - Graded inverse lexicographic order

KW - Groebner-Shirshov bases

KW - Reidemeister torsion

KW - Schubert calculus

KW - Weyl groups

UR - https://www.scopus.com/pages/publications/85091767970

U2 - 10.3934/math.2020484

DO - 10.3934/math.2020484

M3 - Article

AN - SCOPUS:85091767970

SN - 2473-6988

VL - 5

SP - 7562

EP - 7581

JO - AIMS Mathematics

JF - AIMS Mathematics

IS - 6

ER -

On reidemeister torsion of flag manifolds of compact semisimple lie groups

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Keywords

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