On closed manifolds admitting an Anosov diffeomorphism but no expanding map

نویسندگان

چکیده

A few years ago, the first example of a closed manifold admitting an Anosov diffeomorphism but no expanding map was given. Unfortunately, this is not explicit and high-dimensional, although its exact dimension unknown due to type construction. In paper, we present family concrete 12-dimensional nilmanifolds with map, where nilmanifold defined as quotient 1-connected nilpotent Lie group by cocompact lattice. We show that has smallest possible in class infra-nilmanifolds, which conjectured be only manifolds diffeomorphisms up homeomorphism. The proof shows how construct positive gradings from eigenvalues under some additional assumptions related rank, using action Galois on these algebraic units.

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ژورنال

عنوان ژورنال: Journal of Pure and Applied Algebra

سال: 2023

ISSN: ['1873-1376', '0022-4049']

DOI: https://doi.org/10.1016/j.jpaa.2022.107247