Anosov diffeomorphisms on infra-nilmanifolds modeled on a free 2-step nilpotent Lie group | Zendy

Karel Dekimpe | Zendy; Kelly Verheyen | Zendy

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Anosov diffeomorphisms on infra-nilmanifolds modeled on a free 2-step nilpotent Lie group

Author(s) -

Karel Dekimpe,

Kelly Verheyen

Publication year - 2009

Publication title -

groups geometry and dynamics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.05

H-Index - 25

eISSN - 1661-7215

pISSN - 1661-7207

DOI - 10.4171/ggd/70

Subject(s) - nilpotent , mathematics , lie group , pure mathematics , group (periodic table) , lie theory , central series , nilpotent group , physics , adjoint representation of a lie algebra , lie conformal algebra , quantum mechanics

In this article we study the existence question of Anosov diffeomorphisms on an infra-nilmanifold. After establishing a general existence criterion in terms of the associated holonomy representation, we concentrate on infra-nilmanifolds for which the covering Lie group is a free nilpotent Lie group. In turns out that in this case the criterion obtained before can be reduced drastically. Finally, we completely solve the existence question in case the covering Lie group is free 2-step nilpotent and the holonomy group is abelian. Mathematics Subject Classification (2000). 37D20.

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