1998/02/23 by Radu Todor, Radu Alexandru Todor, Todor, Radu +2
Mathematics · #32L10 #32M99 #Advanced Algebra and Geometry #Advanced Operator Algebra Research #Complex Variables (math.CV) #FOS: Mathematics #Geometric and Algebraic Topology #math.CV #msc:32L10 #msc:32M99
paper · pdf · doi:10.48550/arxiv.math/9802110
9 pages, Latex2e; see also preprint MS-98-003 at http://www.maths.ed.ac.uk/ preprints/; corrected typos, a reference added
openalex publication_date 1998/02/23 · arxiv created 1998/02/24 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 pull-back of a line bundle on the base manifold under some mild hypothesis for the curvature.