Poincaré polynomial and \({SL(2, \mathbb{C})}\) -representation on Kähler manifolds
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Abstract
The cohomology ring of any compact Kähler manifold gives rise to an \({SL(2, \mathbb{C})}\) -representation. In this short note, we show that the character of this representation essentially is the Poincaré polynomial of this Kähler manifold, which gives a natural interpretation of the Poincaré polynomial for Kähler manifolds. Our result is an analogue to an interpretation of the χ y genus for holomorphic symplectic manifolds due to George Thompson.
Mathematics Subject Classification (1991)
53C55Keywords
Kähler manifold Poincaré polynomial \({SL(2, \mathbb{C})}\)-representation CharacterPreview
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