The space of Anosov diffeomorphisms

We consider the space XL of Anosov diffeomorphisms homotopic to a fixed automorphism L of an infranilmanifold M. We show that if M is the 2‐torus T2, then XL is homotopy equivalent to T2. In contrast, if the dimension of M is large enough, then we show that XL is rich in homotopy and has infinitely...

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Bibliographic Details
Published in:Journal of the London Mathematical Society 2014-04, Vol.89 (2), p.383-396
Main Authors: Thomas Farrell, F., Gogolev, Andrey
Format: Article
Language:English
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Summary:We consider the space XL of Anosov diffeomorphisms homotopic to a fixed automorphism L of an infranilmanifold M. We show that if M is the 2‐torus T2, then XL is homotopy equivalent to T2. In contrast, if the dimension of M is large enough, then we show that XL is rich in homotopy and has infinitely many connected components.
ISSN:0024-6107
1469-7750
DOI:10.1112/jlms/jdt073