Work

Hyperbolic Groups and Non-compact Real Algebraic Curves

Year: 2021

Type: article

Abstract: In this paper we study the spaces of non-compact real algebraic curves, i.e. pairs (P, τ), where P is a compact Riemann surface with a finite number of holes and punctures and τ: P → P is an anti-holomorphic involution. We describe the uniformisation of non-compact real algebraic curves by Fuchsian groups. We construct the spaces of non-compact real algebraic curves and describe their connected components. We prove that any connected component is homeomorphic to a quotient of a finite-dimensional real vector space by a discrete group and determine the dimensions of these vector spaces.

Source: Transformation Groups

DOI: 10.1007/s00031-021-09644-1

Authors: SERGEY NATANZON, ANNA PRATOUSSEVITCH

Institutions: National Research University Higher School of Economics, University of Liverpool

Language: English

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,780

Funder: Russian Foundation for Basic Research