On certain enumeration problems in two-dimensional topology

TL;DR

This paper presents solutions to key enumeration problems in surface topology, including classifying sections of fiber bundles and computing non-abelian cohomology, advancing understanding of surface topological structures.

Contribution

It introduces novel methods for enumerating homotopy classes of sections and calculating non-abelian cohomology in surface topology.

Findings

Enumeration of homotopy classes of sections achieved

Non-abelian 1-cohomology of surfaces computed

New techniques for surface topology problems developed

Abstract

We announce a solution to several enumeration problems in topology of surfaces. This includes an enumeration of homotopy classes of sections of locally trivial fiber bundles over surfaces and a computation of non-abelian 1-cohomology of surfaces.