Holomorphic Morse Inequalities on Covering Manifolds
نویسنده
چکیده
The goal of this paper is to generalize Demailly’s asymptotic holomorphic Morse inequalities to the case of a covering manifold of a compact manifold. We shall obtain estimates which involve Atiyah’s “normalized dimension” of the square integrable harmonic spaces. The techniques used are those of Shubin who gave a proof for the usual Morse inequalities in the presence of a group action relying on Witten ideas. As a consequence we obtain estimates for the dimension of the square integrable holomorphic sections of the pullback of a line bundle on the base manifold under some mild hypothesis for the curvature.
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