Rotation Numbers and Isometries |
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Authors: | Konstantin Athanassopoulos |
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Institution: | (1) Department of Mathematics, University of Crete, GR-71409 Iraklion, Greece; e-mail |
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Abstract: | Using the notion of rotation set for homeomorphisms of compact manifolds, we define the rotation homomorphism of a connected compact orientable Riemannian manifold and apply it to prove that the dimension of the isometry group of a connected compact orientable Riemannian 3-manifold without conjugate points is not greater than its first Betti number. In higher dimensions the same is true under the additional assumption that the fundamental cohomology class of the manifold is a cup product of integral 1-dimensional classes. |
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Keywords: | asymptotic cycle rotation homomorphism manifold without conjugate points |
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