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One of best ways for quantization of Kahler varieties is to use Kahler reduction since quantization commutes with reduction.

so you can write Teichmuller space $\mathcal T(M)$ by symplectic reduction,

$$\mu^{-1}(0)/Diff^+M\cong\mathfrak{Met}_{-1}(M)/Diff^+M=\mathcal T(M)$$

which $\mathfrak{Met}_{-1}M$ is the space of reimannian metrics of constant scalar curvature $-1$. Hence has $\omega_{WP}$ Weil-Petersson metric.

see page 12 http://arxiv.org/pdf/math/0507076.pdf

For example for quantization of coadjoint orbit, you need to quantize $T^*G$, since coadjoint orbit is just symplectic quotient of $T^*G$. See http://fr.slideshare.net/HassanJolany/geometric-quantization-on-coadjoint-orbits

One of best ways for quantization of Kahler varieties is to use Kahler reduction since quantization commutes with reduction.

so you can write Teichmuller space $\mathcal T(M)$ by symplectic reduction,

$$\mu^{-1}(0)/Diff^+M\cong\mathfrak{Met}_{-1}(M)/Diff^+M=\mathcal T(M)$$

which $\mathfrak{Met}_{-1}M$ is the space of reimannian metrics of constant scalar curvature $-1$. Hence has $\omega_{WP}$ Weil-Petersson metric.

see page 12 http://arxiv.org/pdf/math/0507076.pdf

and also nice paper of Maryam Mirzakhani pages 8-9 http://www.ams.org/journals/jams/2007-20-01/S0894-0347-06-00526-1/S0894-0347-06-00526-1.pdf

For example for quantization of coadjoint orbit, you need to quantize $T^*G$, since coadjoint orbit is just symplectic quotient of $T^*G$. See my master project presentation http://fr.slideshare.net/HassanJolany/geometric-quantization-on-coadjoint-orbits

One of best ways for quantization of Kahler varieties is to use Kahler reduction since quantization commutes with reduction.

so you can write Teichmuller space by symplectic reduction, see

http://link.springer.com/article/10.1007%2Fs10711-007-9223-z

For example for quantization of coadjoint orbit, you need to quantize $T^*G$, since coadjoint orbit is just symplectic quotient of $T^*G$. See http://fr.slideshare.net/HassanJolany/geometric-quantization-on-coadjoint-orbits

One of best ways for quantization of Kahler varieties is to use Kahler reduction since quantization commutes with reduction.

so you can write Teichmuller space $\mathcal T(M)$ by symplectic reduction,

$$\mu^{-1}(0)/Diff^+M\cong\mathfrak{Met}_{-1}(M)/Diff^+M=\mathcal T(M)$$

which $\mathfrak{Met}_{-1}M$ is the space of reimannian metrics of constant scalar curvature $-1$. Hence has $\omega_{WP}$ Weil-Petersson metric.

see page 12 http://arxiv.org/pdf/math/0507076.pdf

For example for quantization of coadjoint orbit, you need to quantize $T^*G$, since coadjoint orbit is just symplectic quotient of $T^*G$. See http://fr.slideshare.net/HassanJolany/geometric-quantization-on-coadjoint-orbits

One of best ways for quantization of Kahler varieties is to use Kahler reduction since quantization commutes with reduction.

so you can write Teichmuller space by symplectic reduction, see

http://link.springer.com/article/10.1007%2Fs10711-007-9223-z

One of best ways for quantization of Kahler varieties is to use Kahler reduction since quantization commutes with reduction.

so you can write Teichmuller space by symplectic reduction, see

http://link.springer.com/article/10.1007%2Fs10711-007-9223-z

For example for quantization of coadjoint orbit, you need to quantize $T^*G$, since coadjoint orbit is just symplectic quotient of $T^*G$. See http://fr.slideshare.net/HassanJolany/geometric-quantization-on-coadjoint-orbits