On the de Rham homomorphism for $L_π$-cohomologies
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866916187481309184 |
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| author | Gol'dshtein, V. Panenko, R. |
| author_facet | Gol'dshtein, V. Panenko, R. |
| contents | We study the procedure of regularization in the context of the Lipschitz version of de Rham calculus on metric simplicial complexes with bounded geometry. It provides us with the machinery to handle the de Rham homomorphism for $L_π$-cohomologies. In this respect, we obtain the condition resolving the question of triviality of the kernel for de Rham homomorphism. In particular, we specify the non-trivial cohomology classes explicitly for a sequence of parameters $π= \langle p_0,\,p_1,\dots,\,p_n\rangle$ missing non-increasing monotonicity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_12071 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the de Rham homomorphism for $L_π$-cohomologies Gol'dshtein, V. Panenko, R. Differential Geometry 58A12, 51F30 We study the procedure of regularization in the context of the Lipschitz version of de Rham calculus on metric simplicial complexes with bounded geometry. It provides us with the machinery to handle the de Rham homomorphism for $L_π$-cohomologies. In this respect, we obtain the condition resolving the question of triviality of the kernel for de Rham homomorphism. In particular, we specify the non-trivial cohomology classes explicitly for a sequence of parameters $π= \langle p_0,\,p_1,\dots,\,p_n\rangle$ missing non-increasing monotonicity. |
| title | On the de Rham homomorphism for $L_π$-cohomologies |
| topic | Differential Geometry 58A12, 51F30 |
| url | https://arxiv.org/abs/2312.12071 |