Morse Functions of G2/SO(4)

Yuuki Sasaki

doi:10.3836/tjm/1502179356

Abstract

We construct $\mathbb{Z}_{2}$ -perfect Morse functions of $G_{2}/\mathrm{SO(4)}$ whose set of all critical points is a great antipodal set of $G_{2}/\mathrm{SO(4)}$ . In particular, we give the reason why the $2$ -number $\#_{2}(G_{2}/\mathrm{SO(4)})$ matches the Betti number of the $\mathbb{Z}_{2}$ -coefficient homology group of $G_{2}/\mathrm{SO(4)}$ .

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Yuuki Sasaki. "Morse Functions of $G_{2}/\mathrm{SO(4)}$ ." Tokyo J. Math. 45 (1) 201 - 214, June 2022. https://doi.org/10.3836/tjm/1502179356

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Received: 5 August 2020; Revised: 31 March 2021; Published: June 2022

First available in Project Euclid: 21 February 2022

MathSciNet: MR4484255

zbMATH: 07574171

Digital Object Identifier: 10.3836/tjm/1502179356

Subjects:

Primary: 20G41

Secondary: 53C35 , 58E05

Keywords: antipodal set , Morse function , Symmetric space

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