Título: Gradient map for the action of a real reductive Lie group
Palestrante: Leonardo Biliotti (Università di Parma)
Local: Transmissão online
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ID da reunião: 824 5727 0949
Resumo: We study the action of a real reductive group G on a real submanifold X of a Kahler manifold Z. We suppose that the action of G extends holomorphically to an action of the complexified group G^\C and that with respect to a compatible maximal compact subgroup U of G^\C the action on Z is Hamiltonian. There is a corresponding gradient map μ : X → p where g = k⊕p is a Cartan decomposition of g. Using an Ad(K)-invariant inner product we obtain the norm square of the gradient map. In this talk we investigate convexity properties of the gradient map. We also describe compact orbits of a parabolic subgroup of G. Finally, we investigate the norm square of the gradient map. As an application we prove that a norm square of a two orbit variety M is Morse-Bott obtaining results on the cohomology and the K-invariant cohomology of M. A part of this talk is a joint work with my PhD student Joshua Windare (arXiv:2106.13074, arXiv:2105.05765 and arXiv:2012.14858).
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