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On a Runge theorem over \({\mathbb {R}}_3\)

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Abstract

In this paper, we investigate a topological characterization of the Runge theorem in the Clifford algebra \( {\mathbb {R}}_3\) via the description of the homology groups of axially symmetric open subsets of the quadratic cone in \({\mathbb {R}}_3\).

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Notes

  1. An anti-involution is a linear self-map of order 2 such that \({\overline{xy}}=({{\bar{y}}})\cdot ({{\bar{x}}})\ \forall x,y \ \in A \), with A any real quadratic alternative algebra with a unity.

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Acknowledgements

The authors are grateful to the anonymous referee whose deep and extensive comments greatly contributed to improve this paper.

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Authors and Affiliations

  1. Dipartimento di Matematica e Informatica, Università di Ferrara, Via Machiavelli n. 30, 44121, Ferrara, Italy

    Cinzia Bisi

  2. Dipartimento di Matematica, Politecnico di Milano, Via Bonardi n. 9, 20133, Milan, Italy

    Antonino De Martino

  3. Lehrstuhl Analysis II, Fakultät für Mathematik, Ruhr-Universität Bochum, 44780, Bochum, Germany

    Jörg Winkelmann

Authors
  1. Cinzia Bisi
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  2. Antonino De Martino
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  3. Jörg Winkelmann
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Correspondence to Cinzia Bisi.

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Bisi, C., De Martino, A. & Winkelmann, J. On a Runge theorem over \({\mathbb {R}}_3\). Annali di Matematica 202, 1531–1556 (2023). https://doi.org/10.1007/s10231-022-01291-x

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