Flexible exponents of non-geometric 3-manifolds

Abstract

A classical question in quantitative topology is to bound the mapping degree $\mathrm{deg}(f)$ in terms of its Lipchitz constant $\text{Lip}(f)$. For a closed, orientable, Riemannian manifold $M$, the flexible exponent $\alpha (M)$ is the infimum of $\alpha ⩾0$ such that $|\text{deg}(f)|⩽C\cdot (\text{Lip}(f){)}^{\alpha }$ holds for any Lipschitz map $f:M\to M$. For a geometric 3-manifold $M$ in the sense of Thurston, $\alpha (M)$ is determined in \cite{DLWWW}. In this paper, we determine $\alpha (M)$ for non-geometric 3-manifolds.

18 pages, 5 figures