Algorithms and topological invariants for dynamic systems. III. Algorithms for Recognition and Classification of 2-Dimensional Surfaces
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866909493161361408 |
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| author | Prishlyak, Alexandr |
| author_facet | Prishlyak, Alexandr |
| contents | 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). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_09958 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Algorithms and topological invariants for dynamic systems. III. Algorithms for Recognition and Classification of 2-Dimensional Surfaces Prishlyak, Alexandr Geometric Topology Dynamical Systems 37c10, 37c15, 37c20 G.1.7 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). |
| title | Algorithms and topological invariants for dynamic systems. III. Algorithms for Recognition and Classification of 2-Dimensional Surfaces |
| topic | Geometric Topology Dynamical Systems 37c10, 37c15, 37c20 G.1.7 |
| url | https://arxiv.org/abs/2502.09958 |