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On the de Rham Homomorphism for Lπ-Cohomologies

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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 Lπ-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 nontrivial cohomology classes explicitly for a sequence of parameters π = <p0, p1,…, pn> missing nonincreasing monotonicity.

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Authors and Affiliations

  1. Ben Gurion University of the Negev, P. O. Box 653, Beer Sheva, Israel

    Vladimir Gol’dshtein

  2. Department of Mathematics, Ben Gurion University of the Negev, P. O. Box 653, Beer Sheva, Israel

    Roman Panenko

Authors
  1. Vladimir Gol’dshtein
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  2. Roman Panenko
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Correspondence to Vladimir Gol’dshtein.

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Gol’dshtein, V., Panenko, R. On the de Rham Homomorphism for Lπ-Cohomologies. J Math Sci 281, 646–676 (2024). https://doi.org/10.1007/s10958-024-07142-9

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  • DOI: https://doi.org/10.1007/s10958-024-07142-9

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