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The aim is to explore the role of complex Hopf fibrations in prequantization geometries and their applications in mathematical physics.

June 27, 2026Open Access

Complex Hopf Fibrations as Prequantization Geometries: Categorified Prequantization, Equivariant Spectra, and Higher-Form Reduction

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The aim is to explore the role of complex Hopf fibrations in prequantization geometries and their applications in mathematical physics.
Developed Hopf fibrations as prequantization geometries involving contact and Kähler geometry.
Derived Chern-Weil structures and computed scalar spectra within these geometries.
Constructed higher-form theories and discussed dynamical observables in odd-dimensional manifolds.
Identified explicit relationships between Hopf fibration structures and geometric quantization.
Established new consistency conditions for chiral extensions involving anomaly tests.
Introduced heat-kernel factorization that supports well-defined zeta determinants.

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Develops complex Hopf fibrations for geometric prequantization, suggesting new insights in theoretical physics.

Alfredo Sepulveda-Jimenez (2026) studied this question.

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