Connectedness of fibers beyond semitoric systems I: the non-degenerate case

2024/02/08 by Daniele Sepe, Sepe, Daniele, Susan Tolman +1 · 1 citation
Mathematics · #53D20. Secondary 37J39 #53D35 #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Primary 37J35 #Symplectic Geometry (math.SG)

paper · pdf · doi:10.48550/arxiv.2402.05814

openalex publication_date 2024/02/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we study the connectedness of the fibers of integrable systems that extend complexity one T-spaces with proper moment maps, assuming that every tall singular point is non-degenerate. Our main result states that if there are no tall singular points with a hyperbolic block and connected T-stabilizer, then each fiber is connected. Moreover, we prove that the above condition is necessary if either some reduced space is simply connected or the moment map for the integrable system is generic in a natural sense.

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• Connectedness of fibers beyond semitoric systems II: ephemeral singular points

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