Archiv der Mathematik

, Volume 101, Issue 5, pp 495–499 | Cite as

Poincaré polynomial and \({SL(2, \mathbb{C})}\) -representation on Kähler manifolds



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 χy genus for holomorphic symplectic manifolds due to George Thompson.

Mathematics Subject Classification (1991)



Kähler manifold Poincaré polynomial \({SL(2, \mathbb{C})}\)-representation Character 


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© Springer Basel 2013

Authors and Affiliations

  1. 1.Department of MathematicsTongji UniversityShanghaiChina

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