Non-squeezing property of contact balls

2014/05/31 by Sheng-Fu Chiu · 3 citations
Mathematics · #math.SG

paper · pdf · doi:10.1215/00127094-3715517

published as Duke Math. J. 166, no. 4 (2017), 605-655 · 38 pages

arxiv created 2015/03/31 · arxiv updated 2017/03/15

Abstract

In this paper we solve a contact non-squeezing conjecture proposed by Eliashberg, Kim and Polterovich. Let B_R be the open ball of radius R in R²ⁿ and let R²ⁿ\timesS¹ be the prequantization space equipped with the standard contact structure. Following Tamarkin's idea, we apply microlocal category methods to prove that if R and r satisfy 1≤πr²<πR², then it is impossible to squeeze the contact ball B_R\timesS¹ into B_r\timesS¹ via compactly supported contact isotopies.

Cited by

• On flat translated chains of contactomorphisms of ℝ²ⁿ⁺¹ and ℝ²ⁿ × S¹
• A topological classification of generating functions
• A survey on orderability and contact non-squeezing

Related

• Contact non-squeezing at large scale in \mathbb R²ⁿ × S¹
• Contact non-squeezing at large scale via generating functions
• Contact non-squeezing in various closed prequantizations
• Contact non-squeezing and orderability via the shape invariant
• Non-simplicity of isocontact embeddings in all higher dimensions