On localization and Riemann-Roch numbers for symplectic quotients

1996 ◽  
Vol 47 (185) ◽  
pp. 165-185
Author(s):  
L. Jeffrey
Keyword(s):  
Symplectic Quotients

scholarly journals Corrigendum: Gromov-Witten invariants of symplectic quotients and adiabatic limits

2009 ◽  
Vol 7 (3) ◽  
pp. 377-379
Author(s):  
A. Rita Gaio ◽  
A. Rita Gaio ◽  
Dietmar A. Salamon ◽  
Dietmar A. Salamon
Keyword(s):  
Adiabatic Limits ◽  
Symplectic Quotients

THE KIRWAN MAP FOR SINGULAR SYMPLECTIC QUOTIENTS

2006 ◽  
Vol 73 (01) ◽  
pp. 209-230 ◽  
Author(s):  
YOUNG-HOON KIEM ◽  
JONATHAN WOOLF
Keyword(s):  
Symplectic Quotients

scholarly journals Pushing down the Rumin complex to conformally symplectic quotients

2014 ◽  
Vol 35 ◽  
pp. 255-265 ◽  
Author(s):  
Andreas Čap ◽  
Tomáš Salač
Keyword(s):  
Symplectic Quotients ◽  
Rumin Complex

scholarly journals Symplectic quotients have symplectic singularities

2020 ◽  
Vol 156 (3) ◽  
pp. 613-646 ◽  
Author(s):  
Hans-Christian Herbig ◽  
Gerald W. Schwarz ◽  
Christopher Seaton
Keyword(s):  
Lie Group ◽  
Moment Map ◽  
Compact Lie Group ◽  
The Real ◽  
Level Zero ◽  
Symplectic Quotients ◽  
Complex Symplectic

Let $K$ be a compact Lie group with complexification $G$, and let $V$ be a unitary $K$-module. We consider the real symplectic quotient $M_{0}$ at level zero of the homogeneous quadratic moment map as well as the complex symplectic quotient, defined here as the complexification of $M_{0}$. We show that if $(V,G)$ is $3$-large, a condition that holds generically, then the complex symplectic quotient has symplectic singularities and is graded Gorenstein. This implies in particular that the real symplectic quotient is graded Gorenstein. In case $K$ is a torus or $\operatorname{SU}_{2}$, we show that these results hold without the hypothesis that $(V,G)$ is $3$-large.

INTERSECTION THEORY ON SYMPLECTIC QUOTIENTS OF PRODUCTS OF SPHERES

2001 ◽  
Vol 12 (01) ◽  
pp. 97-111 ◽  
Author(s):  
TATSURU TAKAKURA
Keyword(s):  
Explicit Formula ◽  
Generating Function ◽  
Cohomology Ring ◽  
Geometric Quantization ◽  
Intersection Theory ◽  
Symplectic Reduction ◽  
Poincare Duality ◽  
Diagonal Action ◽  
Symplectic Quotients ◽  
Products Of Spheres

We present an explicit formula for cohomology intersection pairings on an arbitrary smooth symplectic quotient of products of 2-spheres, by the standard diagonal action of SO3, without using known results on relations in the cohomology ring. By the Poincaré duality, it contains all the information enough to recover the structure of the cohomology ring. Our method is based on the commutativity of geometric quantization and symplectic reduction, originating from a conjecture of Guillemin-Sternberg. In fact, it enables us to derive a formula for the generating function of the intersection pairings.

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