Sympletic Reduction and a Weighted Multiplicity Formula for Twisted Spin^c-Dirac Operations

Details Sympletic Reduction and a Weighted Multiplicity Formula for Twisted Spin^c-Dirac Operations Sympletic Reduction and a Weighted Multiplicity Formula for Twisted Spin^c-Dirac Operations

1999-01-21

arxiv.org/abs/math/9901092v1

Asian Journal of Mathematics Volume 2, number 3, pp. 591-608

Mathematics

Geometric Topology

17 pages

Scientific paper

We extend our earlier work in [TZ1], where an analytic approach to the Guillemin-Sternberg conjecture [GS] was developed, to cases where the Spin^c-complex under consideration is allowed to be further twisted by certain exterior power bundles of the cotangent bundle. The main result is a weighted quantization formula in the presence of commuting Hamiltonian actions. The corresponding Morse-type inequalities in holomorphic situations are also established.

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