Bicomplex Characteristic Classes
Abstract
We introduce bicomplex fiber bundles and develop a framework for bicomplex characteristic classes and almost bicomplex structures on smooth manifolds. In the first part, we present the basic definitions and properties of these bundles, including their fundamental idempotent decomposition and the correspondence between their isomorphism classes and homotopy classes of maps into the bicomplex infinite Grassmannian. We then define bicomplex characteristic classes and show that, in general, they are not determined by the Chern classes of the underlying complex bundle. We also construct the bicomplex Chern character and discuss its algebraic properties. Finally, we apply the resulting theory to almost bicomplex manifolds, providing examples and obstructions to the existence of such structures.
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BibTeX
@misc{arcinieganevarez2026bicomplex,
title = {{Bicomplex Characteristic Classes}},
author = {José Antonio Arciniega-Nevárez and Yesenia Bravo-Ortega and Inácio Rabelo and Agustín Romano-Velázquez},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.17692},
eprint = {2609.17692},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.17692},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Bicomplex Characteristic Classes
AU - José Antonio Arciniega-Nevárez
AU - Yesenia Bravo-Ortega
AU - Inácio Rabelo
AU - Agustín Romano-Velázquez
PY - 2026
DA - 2026/09/15
PB - arXiv
DO - 10.48550/arxiv.2609.17692
UR - https://arxiv.org/abs/2609.17692
AB - We introduce bicomplex fiber bundles and develop a framework for bicomplex characteristic classes and almost bicomplex structures on smooth manifolds. In the first part, we present the basic definitions and properties of these bundles, including their fundamental idempotent decomposition and the correspondence between their isomorphism classes and homotopy classes of maps into the bicomplex infinite Grassmannian. We then define bicomplex characteristic classes and show that, in general, they are not determined by the Chern classes of the underlying complex bundle. We also construct the bicomplex Chern character and discuss its algebraic properties. Finally, we apply the resulting theory to almost bicomplex manifolds, providing examples and obstructions to the existence of such structures.
ER -