A bound on the cohomology of quasiregularly elliptic manifolds

• 成果类型: Article
• 署名作者: Prywes, Eden
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2019.189.3.5
• 发表日期: 2019
• 页码: 863-883
• 关键词: quasi-regular mappings; THEOREM

摘要

We show that a closed, connected and orientable Riemannian manifold M of dimension d that admits a nonconstant quasiregular mapping from R-d must have bounded dimension of the cohomology independent of the distortion of the map. The dimension of the degree l de Rham cohomology of M is bounded above by ((d)(l)). This is a sharp upper bound that proves the Bonk-Heinonen conjecture. A corollary of this theorem answers an open problem posed by Gromov in 1981. He asked whether there exists a d-dimensional, simply connected manifold that does not admit a quasiregular mapping from R-d. Our result gives an affirmative answer to this question.