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A nonlinear Lazarev–Lieb theorem: L2-orthogonality via motion planning
Journal of Topology and Analysis  (IF0.457),  Pub Date : 2020-11-21, DOI: 10.1142/s1793525321500060
Florian Frick, Matt Superdock

Lazarev and Lieb showed that finitely many integrable functions from the unit interval to can be simultaneously annihilated in the L2 inner product by a smooth function to the unit circle. Here, we answer a question of Lazarev and Lieb proving a generalization of their result by lower bounding the equivariant topology of the space of smooth circle-valued functions with a certain W1,1-norm bound. Our proof uses a variety of motion planning algorithms that instead of contractibility yield a lower bound for the /2-coindex of a space.