Geometry & Topology Seminar (1/2)

A classical question in quantitative topology is to bound the mapping degree deg⁡(𝑓) in terms of its Lipchitz constant Lip⁡(𝑓). For a closed, oriented manifold 𝑀, the flexible exponent 𝛼⁡(𝑀) is the infimum of 𝛼 ≥0 such that |deg⁡𝑓| ≤𝐶⁢Lip⁢(𝑓)𝛼 holds for all differentiable 𝑓 :𝑀 →𝑀. The flexible exponent measures how effectively a self-mapping can wrap itself.

We give the complete result 𝛼⁡(𝑀) for 3-manifolds 𝑀.

People involved in this work are J. Duan, J. Lin, H. Sun, S. Wang, Z. Wang, D. Wei.