| Title: | Quaternionic Cartan coverings and applications |
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| Authors: | ID Prezelj, Jasna (Author)
ID Vlacci, Fabio (Author) |
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| Files: |  PDF - Presentation file, download (582,39 KB)
MD5: A2733242690288AE8355B831C125CC65
 URL - Source URL, visit https://link.springer.com/article/10.1007/s12220-025-01900-0
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| Language: | English |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: |  IMFM - Institute of Mathematics, Physics, and Mechanics
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| Abstract: | We present the topological foundations for solvability of multiplicative Cousin problems formulated on an axially symmetric domain $\Omega \subset {\mathbb H}$. In particular, we provide a geometric construction of quaternionic Cartan coverings, which are generalizations of (complex) Cartan coverings as presented in Section 4 of Forstnerič and Prezelj (Math. Ann. 322(4), 633-666 (2002)). Because of the requirements of symmetry inherent to the domains of definition of quaternionic regular functions, the existence of quaternionic Cartan coverings of $\Omega$ is not a consequence of the existence of complex Cartan coverings; for the latter, there are no requirements for the symmetries with respect to the real axis. Due to the real axis’s special role, also the covering restricted to $\Omega \cap {\mathbb R}$ must have additional properties. All these required properties were achieved by starting from a particular symmetric tiling of the symmetric set $\Omega \cap ({\mathbb R}+ i{\mathbb R})$. Finally, we apply these results to prove the vanishing of ’antisymmetric’ cohomology groups of planar symmetric domains for $n \ge 2$. |
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| Keywords: | quaternionic Cartan coverings, antisymmetric cohomology groups |
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| Publication status: | Published |
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| Publication version: | Version of Record |
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| Publication date: | 01.03.2025 |
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| Year of publishing: | 2025 |
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| Number of pages: | 25 str. |
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| Numbering: | Vol. 35, iss. 3, [article no.] 80 |
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| PID: | 20.500.12556/DiRROS-21468  |
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| UDC: | 517.5 |
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| ISSN on article: | 1050-6926 |
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| DOI: | 10.1007/s12220-025-01900-0 |
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| COBISS.SI-ID: | 225630467 |
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| Publication date in DiRROS: | 10.02.2025 |
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| Views: | 610 |
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| Downloads: | 298 |
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