Torsion in the full orbifold K-theory of abelian symplectic quotients

Details Torsion in the full orbifold K-theory of abelian symplectic quotients Torsion in the full orbifold K-theory of abelian symplectic quotients

2009-07-29

arxiv.org/abs/0907.5170v3

Geometriae Dedicata. 157, iss. 1 (2012), 187-204

Mathematics

Symplectic Geometry

17 pages, 5 figures. In this final version, technical hypothesis added to the main theorem. This hypothesis is satisfied in al

Scientific paper

Let (M,\omega,\Phi) be a Hamiltonian T-space and let H be a closed Lie subtorus of T. Under some technical hypotheses on the moment map \Phi, we prove that there is no additive torsion in the integral full orbifold K-theory of the orbifold symplectic quotient [M//H]. Our main technical tool is an extension to the case of moment map level sets the well-known result that components of the moment map of a Hamiltonian T-space M are Morse-Bott functions on M. As first applications, we conclude that a large class of symplectic toric orbifolds, as well as certain S^1-quotients of GKM spaces, have integral full orbifold K-theory that is free of additive torsion. Finally, we introduce the notion of semilocally Delzant which allows us to formulate sufficient conditions under which the hypotheses of the main theorem hold. We illustrate our results using low-rank coadjoint orbits of type A and B.

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