Examples of Anosov diffeomorphisms

✍ Scribed by Jorge Lauret

• Publisher: Elsevier Science
• Year: 2003
• Tongue: English
• Weight: 100 KB
• Volume: 262
• Category: Article
• ISSN: 0021-8693
• DOI: 10.1016/s0021-8693(03)00030-9

✦ Synopsis

We prove that if n is any graded rational Lie algebra, then the simply connected nilpotent Lie group N × N with Lie algebra (n ⊗ R) ⊕ (n ⊗ R) has a lattice Γ such that the corresponding nilmanifold (N × N)/Γ admits an Anosov diffeomorphism. This gives a procedure to construct easily several explicit examples of nilmanifolds admitting an Anosov diffeomorphism, and shows that a reasonable classification up to homeomorphism (or even up to commensurability) of such nilmanifolds would not be possible.