A Borsuk-Ulam theorem for Heisenberg group actions

ISSN: 1300-0098
Yayın Aralığı: Yılda 6 Sayı
Yayıncı: TÜBİTAK

Let G = $H_{2n+1}$ be a (2n + 1)-dimensional Heisenberg Lie group acts on M = $C^m$ — {0} and M' = $C^{m'}$ — {0} exponentially. By using Cohomological Index we proved the following theorem. If $f : M rightarrow M'$ is a G-equivariant map, then $mleq m'$.

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[1] Atiyah, M., Bott, R., The Moment Map and Equivariant Cohomology. Topology 23, 1-28(1984).
[2] Fadell, E., Husseini, S.Y., Rabinowitz, P. H., Borsuk-Ulam Theorems for Arbitrary $S^1$ Actions and Applications. Trans. Amer. Math. Soc. 274, 345-360 (1982).
[3], Fadell, E., Husseini, S.Y., Index Theory for Non-compact Group Actions With Applications to Borsuk-Ulam Theorems. Lecture Notes in Math. Springer 1411, 52-68 (1989).
[4] Fadell, E., Husseini, S.Y., An Ideal-valued Cohomological Index Theory With Applications to Borsuk-Ulam and Bourgin- Yang Theorems. Ergodic Theory and Dynamical Systems 8,73-85 (1988).
[5] Fadell, E., Rabinowitz, P. H., Generalized Cohomological Index Theories for Lie Group Action With an Application to Bifurcation Questions for Hamiltonian Systems. Inventiones Mathematica 45, 139-174 (1978).
[6] Husseini, S.Y., Applications of Equivariant Characteristic Classes to Problems of Borsuk- Ulam and Degree Theory Type. To appear in Topology and Its Applications.
[7] Palais, P., On the Existence of Slices for Actions of Non- compact Lie Groups. Annals of Math. 73, 295-323 (1961).
[8] Vanstone,R., Halperin,S., and Greub,W., Connections, Curvature, and Cohomology I, II,III Academic Press 1976.