Pseudo-Anosov Reeb flows and contact structures

2025/12/14 by Julian Chaidez, Chaidez, Julian, Pan, Yijie
Mathematics · Computer Science · #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis #Geometric and Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2512.12698

Abstract

We introduce the notion of a pseudo-Anosov contact structure, which admits a type of singular contact form with pseudo-Anosov Reeb flow. We prove that contact homology detects the free homotopy classes of closed orbits of any pseudo-Anosov Reeb flow and that any pseudo-Anosov contact structure is universally tight and torsion free. Many applications are given, including new cases of the Finiteness Conjecture for transitive pseudo-Anosov flows. Our proofs use a flavor of contact homology graded by a free homotopy class of loops, defined for any contact manifold. We establish several properties of this type of contact homology that may be of independent interest.

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Related

• Pseudo-Anosov flows on hyperbolic L-spaces
• Equivariant symplectic homology of Anosov contact structures
• Local contact homology and applications
• A Smörgåsbord of (bi)contact structures, Reeb flows and pseudo-Anosov flows
• Pseudo-Anosov representatives of stable Hamiltonian structures