Generators and relations found for foam categories.
problem Understanding categories of framed tangled webs and foams.
method Multijet transversality techniques.
result Presentation by generators and relations of categories.
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4 results for “multijets”
The study proves the finiteness of moments for Gaussian field zeros and critical points.
problem Finiteness of moments for Gaussian field zeros and critical points.
method Definition and study of multijets, construction of p-multijet bundles.
result Linear statistics of Gaussian field zeros have finite p-th moments for p ≥ 1.
The square-peg problem is solved using configuration spaces and multijet transversality.
problem Proving that every simple closed curve in the plane has an odd number of inscribed squares.
method Using the multijet transversality theorem and configuration spaces, we find a dense set of smooth embeddings for which the configuration space of points is transverse to any submanifold.
result A dense family of smoothly embedded circles in the plane and in have an odd number of inscribed square-like quadrilaterals.
We prove a transversality "lifting property" for compactified configuration spaces as an application of the multijet transversality theorem: the submanifold of configurations of points on an arbitrary submanifold of Euclidean space may be made transverse to any submanifold of the configuration space of points in Euclid…