Duke Mathematical Journal

Nonsqueezing property of contact balls

Sheng-Fu Chiu

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Abstract

In this paper we solve a contact nonsqueezing conjecture proposed by Eliashberg, Kim, and Polterovich. Let BR be the open ball of radius R in R2n, and let R2n×S1 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 1πr2<πR2, then it is impossible to squeeze the contact ball BR×S1 into Br×S1 via compactly supported contact isotopies.

Article information

Source
Duke Math. J., Volume 166, Number 4 (2017), 605-655.

Dates
Received: 9 June 2014
Revised: 19 May 2016
First available in Project Euclid: 15 November 2016

Permanent link to this document
https://projecteuclid.org/euclid.dmj/1479179169

Digital Object Identifier
doi:10.1215/00127094-3715517

Mathematical Reviews number (MathSciNet)
MR3619302

Zentralblatt MATH identifier
1372.53087

Subjects
Primary: 53D35: Global theory of symplectic and contact manifolds [See also 57Rxx]

Keywords
nonsqueezing contact topology derived category triangulated category microlocal Lagrangian quantization symplectic topology equivariance

Citation

Chiu, Sheng-Fu. Nonsqueezing property of contact balls. Duke Math. J. 166 (2017), no. 4, 605--655. doi:10.1215/00127094-3715517. https://projecteuclid.org/euclid.dmj/1479179169


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