2 papers
math.AT2019
Borsuk-Ulam theorems for products of spheres and Stiefel manifolds revisited
Yu Hin Chan, Shujian Chen, Florian Frick +1
We give a different and possibly more accessible proof of a general Borsuk--Ulam theorem for a product of spheres, originally due to Ramos. That is, we show the non-existence of ce…
math.MG2018
Splitting loops and necklaces: Variants of the square peg problem
Jai Aslam, Shujian Chen, Florian Frick +3
Toeplitz conjectured that any simple planar loop inscribes a square. Here we prove variants of Toeplitz' square peg problem. We prove Hadwiger's 1971 conjecture that any simple loo…