Work

Some counterexamples in surface homology

Year: 2024

Type: article

Abstract: We present four counterexamples in surface homology. The first example shows that even if the loops inducing a homology basis intersect each other at most once, they still may separate the surface into two parts. The other three examples show some difficulties in working with minimal homology bases. Introducing hyperbolic ribbon graphs we modify the examples so as to have a hyperbolic metric.

Source: manuscripta mathematica

DOI: 10.1007/s00229-024-01595-7

Authors: Peter Buser, Eran Makover, Bjoern Muetzel

Institutions: École Polytechnique Fédérale de Lausanne, Central Connecticut State University, Eckerd College

Language: English

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,990

Funder: École Polytechnique Fédérale de Lausanne