Equivariant Index and the Moment Map for Completely Integrable Torus Actions
Equivariant Index and the Moment Map for Completely Integrable Torus Actions
复制标题
完全可积环面动作的等变指数和矩图
DOI：
10.1006/aima.1997.1686
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发表时间：
1998
期刊：
影响因子：
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通讯作者：
Yael Karshon
中科院分区：
文献类型：
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作者：
M. Grossberg;Yael Karshon
考虑紧旋形上的完全可积环面作用。狄拉克算子的等变指标是环面的虚表示，由它所处的权重的多重度决定。我们证明这些多重度等于Duistermaat-Heckman测度的密度函数的值，一旦它被适当地定义。(我们采用的两种形式是线束曲率的一半，它与Spincstructure有关。它是封闭不变的，但不一定是辛的。)我们推导出这些多重度等于“下降矩映射”Φ： M/T→T *的拓扑度，在很好的情况下，它可以被描述为某些圈数的和。
Abstract Consider a completely integrable torus action on a compact Spincmanifold. The equivariant index of the Dirac operator is a virtual representation of the torus and is determined by the multiplicities of the weights which occur it in. We prove that these multiplicities are equal to values of the density function for the Duistermaat–Heckman measure, once this is defined appropriately. (The two-form that we take is half of the curvature of the line bundle which is associated to the Spincstructure. It is closed and invariant but not necessarily symplectic.) We deduce that these multiplicities are equal to the topological degree of the “descended moment map”Φ: M/T→ t *, which in nice cases can be described as sums of certain winding numbers.
环面流形拓扑
DOI：
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发表时间：
2010
期刊：
影响因子：
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作者：
Rappleye;J.;S.Choi
通讯作者：
S.Choi