Manifolds with higher homotopy which do not support anosov diffeomorphisms

Andrey Gogolev; Federico Rodriguez Hertz

doi:10.1112/blms/bdt100

Manifolds with higher homotopy which do not support anosov diffeomorphisms

Andrey Gogolev, Federico Rodriguez Hertz

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Abstract

We show that various classes of closed manifolds with non-trivial higher homotopy groups do not support (transitive) Anosov diffeomorphisms. In particular, we show that a finite product of spheres at least one of which is even-dimensional does not support transitive Anosov diffeomorphisms.

Original language	English (US)
Pages (from-to)	349-366
Number of pages	18
Journal	Bulletin of the London Mathematical Society
Volume	46
Issue number	2
DOIs	https://doi.org/10.1112/blms/bdt100
State	Published - Apr 2014

All Science Journal Classification (ASJC) codes

General Mathematics

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title = "Manifolds with higher homotopy which do not support anosov diffeomorphisms",

abstract = "We show that various classes of closed manifolds with non-trivial higher homotopy groups do not support (transitive) Anosov diffeomorphisms. In particular, we show that a finite product of spheres at least one of which is even-dimensional does not support transitive Anosov diffeomorphisms.",

author = "Andrey Gogolev and Hertz, {Federico Rodriguez}",

note = "Funding Information: The first author was partially supported by the NSF grant DMS-1204943. The second author was partially supported by the NSF grant DMS-1201326. †After finishing our paper we have received a preprint by Kleptsyn and Kudryashov [5] that answers this particular question using similar ideas but in a more convoluted fashion.",

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doi = "10.1112/blms/bdt100",

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AU - Gogolev, Andrey

AU - Hertz, Federico Rodriguez

N1 - Funding Information: The first author was partially supported by the NSF grant DMS-1204943. The second author was partially supported by the NSF grant DMS-1201326. †After finishing our paper we have received a preprint by Kleptsyn and Kudryashov [5] that answers this particular question using similar ideas but in a more convoluted fashion.

PY - 2014/4

Y1 - 2014/4

N2 - We show that various classes of closed manifolds with non-trivial higher homotopy groups do not support (transitive) Anosov diffeomorphisms. In particular, we show that a finite product of spheres at least one of which is even-dimensional does not support transitive Anosov diffeomorphisms.

AB - We show that various classes of closed manifolds with non-trivial higher homotopy groups do not support (transitive) Anosov diffeomorphisms. In particular, we show that a finite product of spheres at least one of which is even-dimensional does not support transitive Anosov diffeomorphisms.

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Manifolds with higher homotopy which do not support anosov diffeomorphisms

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