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<p>The Marsden–Weinstein–Meyer symplectic reduction has an analogous version for cosymplectic manifolds. In this paper, we extend this cosymplectic reduction to the context of groupoids. Moreover, we prove how in the case of an algebroid associated to a cosymplectic groupoid, the integration commutes with the reduction (analogously to what happens in Poisson geometry). On the other hand, we show how the cosymplectic reduction of a groupoid induces a symplectic reduction on a canonical symplectic subgroupoid. Finally, we study what happens to the multiplicative Chern class associated with the <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(S^1\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>S</mi> <mn>1</mn> </msup> </math></EquationSource> </InlineEquation>-central extensions of the reduced groupoid.</p>

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Reduction of cosymplectic groupoids by cosymplectic moment maps

  • 期刊论文

  • 发表日期：

    2025年11月11日

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  • Daniel López Garcia,
  • Nicolas Martinez Alba

摘要

The Marsden–Weinstein–Meyer symplectic reduction has an analogous version for cosymplectic manifolds. In this paper, we extend this cosymplectic reduction to the context of groupoids. Moreover, we prove how in the case of an algebroid associated to a cosymplectic groupoid, the integration commutes with the reduction (analogously to what happens in Poisson geometry). On the other hand, we show how the cosymplectic reduction of a groupoid induces a symplectic reduction on a canonical symplectic subgroupoid. Finally, we study what happens to the multiplicative Chern class associated with the \(S^1\) S 1 -central extensions of the reduced groupoid.