Extensions and Applications of Bredon's Trick in Geometric and Topological Contexts
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866911042012971008 |
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| author | Angel, Mauricio |
| author_facet | Angel, Mauricio |
| contents | We present a comprehensive analysis of Bredon's trick, a powerful local-to-global extension principle with broad applications across differential geometry and computational topology. Our main contributions include: (1) novel applications to stratified pseudomanifolds via Verona cohomology with explicit verification of axiomatic conditions; (2) new frameworks for Ricci flow singularity analysis using local curvature concentration; (3) stability theorems for persistent homology in distributed computational settings; and (4) rigorous applications to medical imaging and neural network topology. By systematically developing the theoretical foundations and providing concrete implementations, this work establishes Bredon's trick as a unifying framework for modern local-to-global arguments in geometric analysis and applied topology. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2507_04512 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Extensions and Applications of Bredon's Trick in Geometric and Topological Contexts Angel, Mauricio Differential Geometry 57N65 (primary), 58A12, 55N33, 53E20 (secondary) We present a comprehensive analysis of Bredon's trick, a powerful local-to-global extension principle with broad applications across differential geometry and computational topology. Our main contributions include: (1) novel applications to stratified pseudomanifolds via Verona cohomology with explicit verification of axiomatic conditions; (2) new frameworks for Ricci flow singularity analysis using local curvature concentration; (3) stability theorems for persistent homology in distributed computational settings; and (4) rigorous applications to medical imaging and neural network topology. By systematically developing the theoretical foundations and providing concrete implementations, this work establishes Bredon's trick as a unifying framework for modern local-to-global arguments in geometric analysis and applied topology. |
| title | Extensions and Applications of Bredon's Trick in Geometric and Topological Contexts |
| topic | Differential Geometry 57N65 (primary), 58A12, 55N33, 53E20 (secondary) |
| url | https://arxiv.org/abs/2507.04512 |