On the topology of loops of contactomorphisms and Legendrians in non-orderable manifolds

2024/06/03 by Luis Hernández–Corbato, Hernández-Corbato, Luis, Javier Martínez-Aguinaga +1 · 1 citation
Mathematics · #53D35 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT) #Mathematical Dynamics and Fractals #Mathematics and Applications #Primary: 53D10. Secondary: 53D22 #Symplectic Geometry (math.SG)

paper · pdf · doi:10.48550/arxiv.2406.01148

openalex publication_date 2024/06/03 · openalex created_date 2024/06/07 · openalex updated_date 2026/07/28

Abstract

We study the global topology of the space \mathcal L of loops of contactomorphisms of a non-orderable closed contact manifold (M²ⁿ⁺¹, α). We filter \mathcal L by a quantitative measure of the ``positivity'' of the loops and describe the topology of \mathcal L in terms of the subspaces of the filtration. In particular, we show that the homotopy groups of \mathcal L are subgroups of the homotopy groups of the subspace of positive loops \mathcal L⁺. We obtain analogous results for the space of loops of Legendrian submanifolds in (M²ⁿ⁺¹, α).

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