Partially hyperbolic diffeomorphisms of 3-manifolds with Abelian fundamental groups

Dmitri Burago, Sergei Ivanov

Research output: Contribution to journalArticle

23 Citations (Scopus)

Abstract

We present the first known nontrivial topological obstructions to the existence of partially hyperbolic diffeomorphisms. In particular, we show that there are no partially hyperbolic diffeomorphisms on the 3-sphere. More generally, we show that for a partially hyperbolic diffeomorphismof a 3-manifoldwith an Abelian fundamental group, the induced action in the first homology group is partially hyperbolic. This improves the results of [4] by dropping the assumption of dynamical coherence.

Original languageEnglish (US)
Pages (from-to)541-580
Number of pages40
JournalJournal of Modern Dynamics
Volume2
Issue number4
DOIs
StatePublished - Dec 1 2008

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Diffeomorphisms
Fundamental Group
Abelian group
Homology Groups
Obstruction

All Science Journal Classification (ASJC) codes

  • Analysis
  • Algebra and Number Theory
  • Applied Mathematics

Cite this

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Partially hyperbolic diffeomorphisms of 3-manifolds with Abelian fundamental groups. / Burago, Dmitri; Ivanov, Sergei.

In: Journal of Modern Dynamics, Vol. 2, No. 4, 01.12.2008, p. 541-580.

Research output: Contribution to journalArticle

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