Search results for "Tubular neighborhood"
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Voisinages tubulaires épointés et homotopie stable à l'infini
2022
We initiate a study of punctured tubular neighborhoods and homotopy theory at infinity in motivic settings. We use the six functors formalism to give an intrinsic definition of the stable motivic homotopy type at infinity of an algebraic variety. Our main computational tools include cdh-descent for normal crossing divisors, Euler classes, Gysin maps, and homotopy purity. Under-adic realization, the motive at infinity recovers a formula for vanishing cycles due to Rapoport-Zink; similar results hold for Steenbrink's limiting Hodge structures and Wildeshaus' boundary motives. Under the topological Betti realization, the stable motivic homotopy type at infinity of an algebraic variety recovers…
On the volume of unit vector fields on spaces of constant sectional curvature
2004
A unit vector field X on a Riemannian manifold determines a submanifold in the unit tangent bundle. The volume of X is the volume of this submanifold for the induced Sasaki metric. It is known that the parallel fields are the trivial minima.