Find Paper, Faster
Example：10.1021/acsami.1c06204 or Chem. Rev., 2007, 107, 2411-2502
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 $ℂ$ 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 $ℤ/2$-coindex of a space.