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<p>Link spectral invariants were introduced by Cristofaro-Gardiner, Humilière, Mak, Seyfaddini, and Smith. They induce Hofer–Lipschitz quasimorphisms on the group of Hamiltonian diffeomorphisms of the two-dimensional sphere. We prove that some linear combinations of those quasimorphisms vanish on the stabiliser of the equator. As a consequence, at least one of the following statements holds: there are non-trivial linear relations between the link quasimorphisms, or the space of equators of the sphere has infinite Hofer diameter. The proof relies on an ‘almost’ Künneth formula in Link Floer Homology for some specific type of connected sums.</p>

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On link quasimorphisms on the sphere and the equator conjecture

  • 期刊论文

  • 发表日期：

    2026年6月30日

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  • Baptiste Serraille,
  • Ibrahim Trifa

摘要

Link spectral invariants were introduced by Cristofaro-Gardiner, Humilière, Mak, Seyfaddini, and Smith. They induce Hofer–Lipschitz quasimorphisms on the group of Hamiltonian diffeomorphisms of the two-dimensional sphere. We prove that some linear combinations of those quasimorphisms vanish on the stabiliser of the equator. As a consequence, at least one of the following statements holds: there are non-trivial linear relations between the link quasimorphisms, or the space of equators of the sphere has infinite Hofer diameter. The proof relies on an ‘almost’ Künneth formula in Link Floer Homology for some specific type of connected sums.