On compact complex surfaces with finite homotopy rank-sum
Algebraic Geometry
2024-08-09 v1 Complex Variables
Geometric Topology
Abstract
A topological space (not necessarily simply connected) is said to have finite homotopy rank-sum if the sum of the ranks of all higher homotopy groups (from the second homotopy group onward) is finite. In this article, we characterize the smooth compact complex Kaehler surfaces having finite homotopy rank-sum. We also prove the Steinness of the universal cover of these surfaces assuming holomorphic convexity of the universal cover.
Cite
@article{arxiv.2408.04558,
title = {On compact complex surfaces with finite homotopy rank-sum},
author = {Indranil Biswas and Buddhadev Hajra},
journal= {arXiv preprint arXiv:2408.04558},
year = {2024}
}
Comments
Final version; Proc. Amer. Math. Soc. (to appear)