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We define and explore the notion of linear weightings for vector bundles,extending the recent work by Loizides and Meinrenken. We construct weightednormal bundles and deformation spaces in the category of vector bundles. Weexplain how a linear weighting determines a filtration on differentialoperators, and an interpolation between a differential operator and its``weighted" linearization. We close by explaining how our constructions capturethe rescaled spinor bundle of Higson and Yi, and a related construction by\v{S}evera.

Linear Weightings and Deformations of Vector Bundles