Anosov automorphisms on certain classes of nilmanifolds
نویسنده
چکیده
We give a necessary and sufficient condition for k-step nilmanifolds associated with graphs (k ≥ 3) to admit Anosov automorphisms. We also prove nonexistence of Anosov automorphisms on certain classes of 2-step and 3-step nilmanifolds. 2000 Mathematics Subject Classification. Primary 37D20; Secondary 22E25
منابع مشابه
Anosov Lie Algebras and Algebraic Units in Number Fields
The nilmanifolds admitting Anosov automorphisms correspond to Anosov Lie algebras, which in turn determine very special algebraic units in number fields. By studying properties of these algebraic units using basic field theory, we can rule out many possibilities for a Lie algebra to be Anosov. This technique is useful for the classification of Anosov Lie algebras and hence the classification of...
متن کاملAnosov Automorphisms on Compact Nilmanifolds Associated with Graphs
We associate with each graph (S, E) a 2-step simply connected nilpotent Lie group N and a lattice Γ in N . We determine the group of Lie automorphisms of N and apply the result to describe a necessary and sufficient condition, in terms of the graph, for the compact nilmanifold N/Γ to admit an Anosov automorphism. Using the criterion we obtain new examples of compact nilmanifolds admitting Anoso...
متن کاملHyperbolic Automorphisms and Anosov Diffeomorphisms on Nilmanifolds
We translate the problem of finding Anosov diffeomorphisms on a nilmanifold which is covered by a free nilpotent Lie group into a problem of constructing matrices in GL(n,Z) whose eigenvalues satisfy certain conditions. Afterwards, we show how this translation can then be solved in some specific situations. The paper starts with a section on polynomial permutations of QK , a subject which is of...
متن کاملTightness and efficiency of irreducible automorphisms of handlebodies
Among (isotopy classes of) automorphisms of handlebodies those called irreducible (or generic) are the most interesting, analogues of pseudo-Anosov automorphisms of surfaces. We consider the problem of isotoping an irreducible automorphism so that it is most efficient (has minimal growth rate) in its isotopy class. We describe a property, called tightness, of certain invariant laminations, whic...
متن کاملNILPOTENCY AND SOLUBILITY OF GROUPS RELATIVE TO AN AUTOMORPHISM
In this paper we introduce the concept of α-commutator which its definition is based on generalized conjugate classes. With this notion, α-nilpotent groups, α-solvable groups, nilpotency and solvability of groups related to the automorphism are defined. N(G) and S(G) are the set of all nilpotency classes and the set of all solvability classes for the group G with respect to different automorphi...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2008