【摘要】
A classical question in quantitative topology is to bound the mapping degree in terms of its Lipchitz constant. In this talk, I will focus on self-maps on geometric 3-manifolds. We will bound the mapping degree by a suitable power of the Lipchitz constant. To get the optimal bound, we will construct the so-called "Legendrian map" on Seifert manifolds, a self map that sends all Seifert fibers to Legendrian knots (of the canonical contact structure) simultaneously. We will also show that such map can never be a diffeomorphism. This is based on a joint work with Jianru Duan, Shicheng Wang, Zhongzi Wang and Dongyi Wei.
