Geometric–Topological Model of the Electron asa Mobius-Type Soliton in Quantum Vacuum

We propose a geometric–topological model in which the electron isdescribed as a stable Dirac soliton residing on a M¨obius-type manifoldembedded in a structured quantum vacuum. Starting from the nonorientable topology of the M¨obius strip, we show that spin-1/2, chargequantization, the gyromagnetic ratio g = 2, and electron–positron duality emerge naturally from anti-periodic boundary conditions and thecurvature-induced spin connection. The model incorporates the da Costageometric potential and the full relativistic Dirac operator on the curvedmanifold, predicting a curvature-induced quantum spin-Hall effect. Recent bottom-up synthesis of M¨obius carbon nanobelts and numerical studies of Dirac fermions on graphene M¨obius strips provide promising experimental analogs for testing the key predictions.