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

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

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

Access to Document

10.1112/blms/bdt100

Cite this

@article{bb535c9ef6764e6eaf39107bbc589dd0,

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.",

year = "2014",

month = apr,

doi = "10.1112/blms/bdt100",

language = "English (US)",

volume = "46",

pages = "349--366",

journal = "Bulletin of the London Mathematical Society",

issn = "0024-6093",

publisher = "John Wiley and Sons Ltd",

number = "2",

}

TY - JOUR

T1 - Manifolds with higher homotopy which do not support anosov diffeomorphisms

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.

UR - https://www.scopus.com/pages/publications/84896931397

UR - https://www.scopus.com/pages/publications/84896931397#tab=citedBy

U2 - 10.1112/blms/bdt100

DO - 10.1112/blms/bdt100

M3 - Article

AN - SCOPUS:84896931397

SN - 0024-6093

VL - 46

SP - 349

EP - 366

JO - Bulletin of the London Mathematical Society

JF - Bulletin of the London Mathematical Society

IS - 2

ER -

Manifolds with higher homotopy which do not support anosov diffeomorphisms

Abstract

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this