The involutions of the compact symmetric spaces
type: Item
instance of: scholarly article
title: The involutions of the compact symmetric spaces
zbMATH Open document ID: 0655.53041
author: Tadashi Nagano
published in: Tokyo Journal of Mathematics
publication date: 1988-01-01T00:00:00Z
review text: The main purpose of this paper is to determine the fixed point sets of the involutions of the compact symmetric spaces. (Here, an involution is any involutive diffeomorphism which commutes with the symmetries of the given space.) The main geometric tool is attaching to any compact symmetric space a couple (M \(+,M\)-) of symmetric subspaces, which was introduced by \textit{B. Y. Chen} and the present author [see Duke Math. J. 44, 745-755 (1977; Zbl 0368.53038) and 45, 405-425 (1978; Zbl 0384.53024)]. Here M \(+\) means a connected component of the fixed point set with respect to a usual symmetry and M - is its ``orthogonal complement'' in a good sense. The author presents interesting relations to various topological and geometrical concepts and problems, such as the determination of the signature \(\tau\) (M), the Bott periodicity, the Chow arithmetic distance, and the Radon duality.
Mathematics Subject Classification ID: 53C35
zbMATH DE Number: 4069752
zbMATH Keywords: fixed point sets
zbMATH Keywords: involutions
zbMATH Keywords: compact symmetric spaces
zbMATH Keywords: signature
zbMATH Keywords: Bott periodicity
zbMATH Keywords: Chow arithmetic distance
zbMATH Keywords: Radon duality
reviewed by: Oldřich Kowalski
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.3836/tjm/1270134261
OpenAlex ID: W4248841499
DOI: 10.3836/TJM/1270134261
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description: scientific article; zbMATH DE number 4069752