On the cohomology of $L^2$-harmonic forms of an incomplete Riemannian manifold
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866917148313518080 |
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| author | Bei, Francesco Spreafico, Mauro |
| author_facet | Bei, Francesco Spreafico, Mauro |
| contents | Motivated by the work of Cappell, Deturck, Gluch and Miller, we extend the notion of cohomology of harmonic forms (of a compact manifold with boundary) to the abstract setting of Hilbert complexes. Then, we present some geometric applications of our construction to incomplete Riemannian manifolds with particular interest to the case of smoothly stratified Thom-Mather spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_13854 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the cohomology of $L^2$-harmonic forms of an incomplete Riemannian manifold Bei, Francesco Spreafico, Mauro Differential Geometry Geometric Topology Motivated by the work of Cappell, Deturck, Gluch and Miller, we extend the notion of cohomology of harmonic forms (of a compact manifold with boundary) to the abstract setting of Hilbert complexes. Then, we present some geometric applications of our construction to incomplete Riemannian manifolds with particular interest to the case of smoothly stratified Thom-Mather spaces. |
| title | On the cohomology of $L^2$-harmonic forms of an incomplete Riemannian manifold |
| topic | Differential Geometry Geometric Topology |
| url | https://arxiv.org/abs/2512.13854 |