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<p>For any compact connected Lie group <i>G</i>, we study the Hamiltonian sum of two compact Hamiltonian group G-manifolds (<i>X</i><sup>+</sup>, <i>ω</i><sup>+</sup>, <i>μ</i><sup>+</sup>) and (<i>X</i><sup>−</sup>, <i>ω</i><sup>−</sup>, <i>μ</i><sup>−</sup>) along a common codimension 2 Hamiltonian submanifold <i>Z</i> with the opposite equivariant Euler classes of the normal bundles. We establish that the symplectic reduction of the Hamiltonian sum agrees with the symplectic sum of the reduced symplectic manifolds. We also compare the equivariant first Chern class of the Hamiltonian sum with the equivariant first Chern classes of <i>X</i><sup>±</sup>.</p>

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The sum of Hamiltonian manifolds

  • 期刊论文

  • 发表日期：

    2025年7月23日

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  • Bohui Chen,
  • Hai-Long Her,
  • Bai-Ling Wang

摘要

For any compact connected Lie group G, we study the Hamiltonian sum of two compact Hamiltonian group G-manifolds (X+, ω+, μ+) and (X−, ω−, μ−) along a common codimension 2 Hamiltonian submanifold Z with the opposite equivariant Euler classes of the normal bundles. We establish that the symplectic reduction of the Hamiltonian sum agrees with the symplectic sum of the reduced symplectic manifolds. We also compare the equivariant first Chern class of the Hamiltonian sum with the equivariant first Chern classes of X±.