English

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.

Keywords

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)

R2 v1 2026-06-28T18:07:52.147Z