Differential Geometry of Weightings.
2020
We describe the notion of a weighting along a submanifold $N\subset M$, and explore its differential-geometric implications. This includes a discussion of weighted normal bundles, weighted deformation spaces, and weighted blow-ups. We give applications to manifolds with (singular) Lie filtrations, recovering and generalizing constructions of van Erp-Yuncken, Choi-Ponge, and Haj-Higson of the `osculating tangent bundle' and related concepts.
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