Sympletic Reduction and a Weighted Multiplicity Formula for Twisted Spinc-Dirac Operations
Abstract
We extend our earlier work in [TZ1], where an analytic approach to the Guillemin-Sternberg conjecture [GS] was developed, to cases where the Spinc-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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