Bott Generator and Its Application to an Almost Complex Structure on S ⁶ *

Abstract

The Bott generator of the homotopy group π _2k−1U(∞) is used to construct an almost complex structure on S ⁶, which is integrable except a small neighborhood.

Keywords

Bott generator / Almost complex structure / Integrability / 32Q99 / 53C15

References

[1] Atiyah Comm. Pure Appl. Math., 1967, 20: 237

[2] Atiyah, M. F., Anomalies and Index Theory, Lecture Notes in Phy., Springer-Verlag, 208, 1984, 313–322

[3] Bott Ann. of Math., 1959, 70: 313

[4] Kervaire Illinois J. of Math., 1960, 4: 161

[5] Peng Acta Math. Sin., 2005, 21: 1459

[6] Steenrod, N., The Topology of Fiber Bundles, Princeton Univ. Press, Princeton, New Jersey, 1974