Quantization Formula for Symplectic Manifolds with Boundary |
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Authors: | Y. Tian W. Zhang |
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Affiliation: | (1) CUNY Graduate Center and NYU Courant Institute, New York, USA, US;(2) Nankai Inst. of Math., Nankai University, Tianjin 300071, People's Republic of China, e-mail: weiping@sun.nankai.edu.cn, CN |
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Abstract: | We extend our earlier work in [TiZ1], where an analytic approach to the Guillemin-Sternberg geometric quantization conjecture [GuSt] was developed, to the case of manifolds with boundary. We also give a general quantization formula that works for both regular and singular reductions. As simple applications, we prove an analytic analogue of the relative residue formula of Guillemin-Kalkman [GuK] and Martin [M], as well as a Guillemin-Sternberg type formula for singular reductions under circle actions. Submitted: February 1997, revised: January 1998 and July 1998, final version: March 1999. |
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