The hodge number is the analog of the betti number on real manifolds for complex manifolds.

On kahler manifolds tex2html_wrap89 This is because tex2html_wrap90 tex2html_wrap91

Also: tex2html_wrap92 which is the poincare duality.

On complex closed kahler manifolds tex2html_wrap93 is even and tex2html_wrap94 so tex2html_wrap95 .

on tex2html_wrap96 , tex2html_wrap97 . so this is sort of a minimal topology for kahler manifolds.

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