3 problems

A compact Lie group acts smoothly on the 3-sphere $S^3$. Linearity conjecture. Every such action is conjugate to a linear action. This asserts that, despite the existence of non-li…

Let $\mathcal{L}\mathbb S^3(\varepsilon_1,\varepsilon_2)$ denote the indicated spaces of locally convex curves on the 3-sphere, where each…

Let $\mathcal{L}\mathbb S^3(\mathbf{1},-\mathbf{1})$ be the space of locally convex curves on the 3-sphere with the indicated endpoint data, let $L$ denote the associated map to cu…