Artículos de revistas
Suspending The Cartan Embedding Of ℍpn Through Spindles And Generators Of Homotopy Groups
Registro en:
Results In Mathematics. , v. 60, n. 1, p. 255 - 263, 2011.
14226383
10.1007/s00025-011-0185-y
2-s2.0-80052915476
Autor
Duran C.E.
Puttmann T.
Rigas A.
Institución
Resumen
We provide an equivariant suspension of the Cartan embedding of the symmetric space S4n+3 → ℍPn {right arrow, hooked} Sp(n+1); this construction furnishes geometric generators of the homotopy group of π4n+6Sp(n + 1). We study the topology and geometry of the image of this generator; in particular we show that it is a spindle, minimal with respect to the biinvariant metric from Sp(n + 1). This spindle also admits a different metric of positive curvature away from the cone singular point. © 2011 Springer Basel AG. 60 1 255 263 Abresch, U., Durán, C.E., Püttmann, T., Rigas, A., Wiedersehen metrics and exotic involutions of Euclidean spheres (2007) J. Reine Angew. Math., 605, pp. 1-21 Abresch, U., Durán, C.E., Püttmann, T., Rigas, A., An Exotic Involution of the 5-sphere, Quicktime Movie, , http://homepage.ruhr-uni-bochum.de/Thomas.Puettmann/XInvolution.html Balinskaya, I.S., Minimal cones of the adjoint action of classical Lie groups (1986) Russ. Math. Surv., 41, pp. 201-202 Bott, R., The stable homotopy of the classical groups (1959) Ann. Math. (2), 70, pp. 313-337 Bryant, R., Personal Communication Durán, C.E., Pointed Wiedersehen metrics on exotic spheres and diffeomorphisms of S6 (2001) Geom. Dedic., 88 (1-3), pp. 199-210 Durán, C.E., Rigas, A., Equivariant homotopy and deformations of diffeomorphisms (2009) Differ. Geom. Appl., 27 (2), pp. 206-211 Durán, C.E., Mendoza, A., Rigas, A., Blakers-Massey elements and exotic diffeomorphisms of S6 and S14 (2004) Trans. Am. Math. Soc., 356 (12), pp. 5025-5043 Fomenko, A.T., (1990) Variational Principles in Topology, Mathematics and Its Applications, Vol. 42, , Dordrecht: Kluwer Gorodski, C., Enlarging totally geodesic submanifolds of symmetric spaces to minimal submanifolds of one dimension higher (2004) Proc. Am. Math. Soc., 132, pp. 2441-2447 Gromoll, D., Meyer, W., An exotic sphere with non-negative sectional curvature (1972) Ann. Math., 96 (2), pp. 413-443 Helgason, S., (1978) Differential Geometry, Lie Groups, and Symmetric Spaces, , New York: Academic Press Inc. [Harcourt Brace Jovanovich Publishers] Hsiang, W.-Y., Lawson, H.B., Minimal submanifolds of low cohomogeneity (1971) J. Diff. Geom., 5, pp. 1-38 Quast, P., Spindles' in symmetric spaces (2006) J. Math. Soc. Japan, 58 (4), pp. 985-994 Püttmann, T., (2004) Some Homotopy Groups of the Classical Groups From a Geometric Viewpoint, , Habilitation thesis, Bochum Püttmann, T., Rigas, A., Presentations of the first homotopy groups of the unitary groups (2003) Comment. Math. Helv., 78 (3), pp. 648-662 Rigas, A., Geodesic spheres as generators of πq(O), πq+1(BO) (1978) J. Diff. Geom., 13 (4), pp. 527-545 Toda, H., (1962) Composition Methods in the Homotopy Groups of Spheres. Annals of Mathematics Studies, Vol. 49, , Princeton: Princeton University Press