Year: 2025
Type: article
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 consider Stein spaces of arbitrary dimension satisfying the above rational homotopy theoretic property, although most of this article focuses on Stein surfaces only. We characterize all Stein surfaces satisfying the finite homotopy rank-sum property. In particular, if such a Stein surface is affine and every element of its fundamental group is finite, it is either simply connected or has a fundamental group of order 2. A detailed classification of the smooth complex affine surfaces of the non-general type satisfying the finite homotopy rank-sum property is obtained. It turns out that these affine surfaces are Eilenberg–MacLane spaces whenever the fundamental group is infinite.
Source: Forum Mathematicum
Authors: Indranil Biswas, Buddhadev Hajra
Institutions: Shiv Nadar University, Tata Institute of Fundamental Research
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4408919724