Dylan Cant

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Extensible positive loops and vanishing of symplectic cohomology

Dylan Cant、Jakob Hedicke、Eric Kilgore

2023年12月。已接受，发表于 Alg. Geom. Topol.

摘要：

The symplectic cohomology of certain symplectic manifolds $W$ with non-compact ends modelled on the positive symplectization of a compact contact manifold $Y$ is shown to vanish whenever there is a positive loop of contactomorphisms of $Y$ which extends to a loop of Hamiltonian diffeomorphisms of $W$. An open string version of this result is also proved: the wrapped Floer cohomology of a Lagrangian $L$ with ideal Legendrian boundary $Λ$ is shown to vanish if there is a positive loop $Λ_{t}$ based at $Λ$ which extends to an exact loop of Lagrangians based at $L$. Various examples of such loops are considered. Applications include the construction of exotic compactly supported symplectomorphisms and exotic fillings of $Λ$.

链接：

• PDF
• arXiv:2311.18267
• BibTeX

  @unpublished{extensible-positive-loops,
    author        = {Dylan Cant and Jakob Hedicke and Eric Kilgore},
    title         = {Extensible positive loops and vanishing of symplectic cohomology},
    note          = {To appear in Alg. Geom. Topol.},
    year          = {2023},
    eprint        = {2311.18267},
    archivePrefix = {arXiv},
    primaryClass  = {math.SG},
  }