Osaka Journal of Mathematics

Borsuk-Ulam type theorems on Stiefel manifolds

Akira Inoue

Full-text: Open access


In this paper, we study the degree of equivariant maps between Stiefel manifolds by using cohomological index theory. As applications, we have some Borsuk-Ulam type theorems on Stiefel manifolds.

Article information

Osaka J. Math., Volume 43, Number 1 (2006), 183-191.

First available in Project Euclid: 28 April 2006

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 55N20: Generalized (extraordinary) homology and cohomology theories
Secondary: 57S17: Finite transformation groups


Inoue, Akira. Borsuk-Ulam type theorems on Stiefel manifolds. Osaka J. Math. 43 (2006), no. 1, 183--191.

Export citation


  • H. Cartan and S. Eilenberg: Homological Algebra, Princeton University Press, 1956.
  • E. Fadell and S. Husseini: An ideal-valued cohomological index theory with applications to Borsuk-Ulam and Bourgin-Yang theorems, Ergodic Theory Dynamical Systems 8 (1988), 73--85.
  • E. Fadell: Ideal-valued generalizations of Ljusternik-Schnierlmann category, with applications; in Topics in Equivariant Topology, (eds. E. Fadell, et al.), Sém. Math. Sup. 108, Press Univ. Montréal, Montréal, 1989, 11--54.
  • Y. Hara: The degree of equivariant maps, Topology Appl. 148 (2005), 113--121.
  • J. Jaworowski: Maps of Stiefel manifolds and a Borsuk-Ulam theorem, Proc. Edinb. Math. Soc. 32 (1989), 271--279.
  • K. Komiya: Borsuk-Ulam theorem and Stiefel manifolds, J. Math. Soc. Japan 45 (1993), 611--626.
  • E. Spanier: Algebraic Topology, McGraw-Hill, New York, 1966.