Algorithms and topological invariants for dynamic systems. III. Algorithms for Recognition and Classification of 2-Dimensional Surfaces

Alexandr Prishlyak

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arXiv · 2502.09958

Algorithms and topological invariants for dynamic systems. III. Algorithms for Recognition and Classification of 2-Dimensional Surfaces

Alexandr Prishlyak

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Abstract

We construct algorithms and topological invariants that allow us to distinguish the topological type of a surface, as well as functions and vector fields for their topological equivalence. In the first part (arXiv:2501.15657), we discused basic concepts of diferential topology. In the second part (arXiv:2502.00506 ) we discused the main discrete topological structures used in the topological theory of dynamic systems. In third part we construct algorithms that allow us recognise 2-manifolds and 3-manifolds in simplicial complexes and regular CW-complex and detreminate topological type for 2-manifolds (connectivity, type of orientability, genus, number of boundary component).

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Alexandr Prishlyak. 2025-02-14. Algorithms and topological invariants for dynamic systems. III. Algorithms for Recognition and Classification of 2-Dimensional Surfaces. https://arxiv.org/abs/2502.09958

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