2 problems

Let $\mathbb{T}^{1}=\mathbb{R}/\mathbb{Z}$, let $\overline{\mathbb{A}}=\mathbb{T}^{1}\times[0,1]$ be the closed annulus, and let…

Let $f:\overline{\mathbb{A}}\to\overline{\mathbb{A}}$ be a homeomorphism preserving Lebesgue measure, let $\widehat{f}$ be a lift, and let $\operatorname{Rot}(\widehat{f})$ be its…