Morse interpolation for hamiltonian gkm spaces

Catalin Zara University of Massachusetts Boston

Differential Geometry mathscidoc:1609.10014

Journal of Differential Geometry, 75, (3), 503-523, 2007
Let M be a compact Hamiltonian T−space, with finite fixed point set MT . An equivariant class is determined by its restriction to MT , and to each fixed point p ∈ MT and generic component of the moment map, there corresponds a canonical class τp. For a special class of Hamiltonian T−spaces, the value τp,q of τp at a fixed point q can be determined through an iterated interpolation procedure, and we obtained a formula for τp,q as a sum over ascending chains from p to q. In general the number of such chains is huge, and the main result of this paper is a procedure to reduce the number of relevant chains, through a systematic degeneration of the interpolation direction. The resulting formula for τp,q resembles, via the localization formula, an integral over a space of chains, and we prove that, for complex Grassmannians, τp,q can indeed be expressed as the integral of an equivariant form over a smooth Schubert variety.
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  author={Catalin Zara},
  booktitle={Journal of Differential Geometry},
Catalin Zara. MORSE INTERPOLATION FOR HAMILTONIAN GKM SPACES. 2007. Vol. 75. In Journal of Differential Geometry. pp.503-523.
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