Anosov diffeomorphisms of products I. Negative curvature and rational homology spheres
2019 ◽
Vol 41
(2)
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pp. 553-569
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Keyword(s):
We show that various classes of products of manifolds do not support transitive Anosov diffeomorphisms. Exploiting the Ruelle–Sullivan cohomology class, we prove that the product of a negatively curved manifold with a rational homology sphere does not support transitive Anosov diffeomorphisms. We extend this result to products of finitely many negatively curved manifolds of dimension at least three with a rational homology sphere that has vanishing simplicial volume. As an application of this study, we obtain new examples of manifolds that do not support transitive Anosov diffeomorphisms, including certain manifolds with non-trivial higher homotopy groups and certain products of aspherical manifolds.
2007 ◽
Vol 142
(2)
◽
pp. 259-268
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2009 ◽
Vol 30
(5)
◽
pp. 1399-1417
Keyword(s):
2008 ◽
Vol 17
(10)
◽
pp. 1199-1221
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1983 ◽
Vol 59
(9)
◽
pp. 445-445
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2005 ◽
Vol 92
(1)
◽
pp. 99-138
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2014 ◽
Vol 07
(01)
◽
pp. 23-46
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2004 ◽
Vol 06
(06)
◽
pp. 833-866
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