Geodesic
Bott periodicity for inclusions of symmetric spaces
Documenta mathematica, Tome 17 (2012), pp. 911-952.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: When looking at Bott's original proof of his periodicity theorem for the stable homotopy groups of the orthogonal and unitary groups, one sees in the background a differential geometric periodicity phenomenon. We show that this geometric phenomenon extends to the standard inclusion of the orthogonal group into the unitary group. Standard inclusions between other classical Riemannian symmetric spaces are considered as well. An application to homotopy theory is also discussed.
Classification : 53C35, 55R45, 53C40
Keywords: symmetric spaces, shortest geodesics, reflective submanifolds, Bott periodicity 
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     author = {Mare, Augustin-Liviu and Quast, Peter},
     title = {Bott periodicity for inclusions of symmetric spaces},
     journal = {Documenta mathematica},
     pages = {911--952},
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     volume = {17},
     year = {2012},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DOCMA_2012__17__a3/}
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Mare, Augustin-Liviu; Quast, Peter. Bott periodicity for inclusions of symmetric spaces. Documenta mathematica, Tome 17 (2012), pp. 911-952. http://geodesic.mathdoc.fr/item/DOCMA_2012__17__a3/