Torsion in the full orbifold K-theory of abelian symplectic quotients - Mathematics > Symplectic GeometryReport as inadecuate




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Abstract: Let M,\omega,\Phi be a Hamiltonian T-space and let H be a closed Liesubtorus of T. Under some technical hypotheses on the moment map \Phi, we provethat there is no additive torsion in the integral full orbifold K-theory of theorbifold symplectic quotient M-H. Our main technical tool is an extension tothe case of moment map level sets the well-known result that components of themoment map of a Hamiltonian T-space M are Morse-Bott functions on M. As firstapplications, we conclude that a large class of symplectic toric orbifolds, aswell as certain S^1-quotients of GKM spaces, have integral full orbifoldK-theory that is free of additive torsion. Finally, we introduce the notion ofsemilocally Delzant which allows us to formulate sufficient conditions underwhich the hypotheses of the main theorem hold. We illustrate our results usinglow-rank coadjoint orbits of type A and B.



Author: Rebecca Goldin, Megumi Harada, Tara S. Holm

Source: https://arxiv.org/







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