The Minimal Dilatation of a Genus-Two Surface

Abstract

We show that the minimal dilatation of pseudo-Anosov homeomorphisms of a closed oriented genus-two surface is equal to the largest root of x ⁴ – x ³ – x ² – x + 1, which is approximately 1.72208.

Keywords:

• Primary 37E30
• Secondary 37B40, 57M60
• dilatation
• pseudo-Anosov homeomorphism
• genus-two surface
• primitive matrix