Tokyo Journal of Mathematics

Intersection of Stable and Unstable Manifolds for Invariant Morse Function

Hitoshi YAMANAKA

Full-text: Open access

Abstract

We study the structure of the smooth manifold which is defined as the intersection of a stable manifold and an unstable manifold for an invariant Morse-Smale function.

Article information

Source
Tokyo J. Math., Volume 36, Number 2 (2013), 513-519.

Dates
First available in Project Euclid: 31 January 2014

Permanent link to this document
https://projecteuclid.org/euclid.tjm/1391177985

Digital Object Identifier
doi:10.3836/tjm/1391177985

Mathematical Reviews number (MathSciNet)
MR3161572

Zentralblatt MATH identifier
1292.57027

Subjects
Primary: 57R70: Critical points and critical submanifolds
Secondary: 57S15: Compact Lie groups of differentiable transformations 37D15: Morse-Smale systems

Citation

YAMANAKA, Hitoshi. Intersection of Stable and Unstable Manifolds for Invariant Morse Function. Tokyo J. Math. 36 (2013), no. 2, 513--519. doi:10.3836/tjm/1391177985. https://projecteuclid.org/euclid.tjm/1391177985


Export citation

References

  • M. Atiyah, Convexity and commuting Hamiltonians, Bull. London Math. Soc. 14 (1982), no. 1, 1–15.
  • A. Banyaga and D. Hurtubise, Lectures on Morse Homology, Kluwer Texts in the Mathematical Sciences, Volume 29 (2004).
  • M. Goresky, R. Kottwitz and MacPherson, Equivariant cohomology, Koszul duality and the localization theorem, Invent. Math. 131 (1998), no. 1, 25–83.
  • J. F. Plante, Fixed points of Lie group actions on surfaces, Ergod. Th. and Dyn. Sys. 6 (1986), 149–161.
  • E. Witten, Supersymmetry and Morse theory, J. Differential Geom. 17 (1982), no. 4, 661–692.