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UID:20250312T173631EDT-7025HeTrUm@132.216.98.100
DTSTAMP:20250312T213631Z
DESCRIPTION:Contact non-squeezing - a low-tech proof in the language of per
 sistence modules.\n\n Viterbo's symplectic capacity of domains in $R^{2n}$
  and Sandon's contact capacity of domains in $R^{2n} imes S^1$ are persist
 ences of certain homology classes in the persistence modules formed by gen
 erating function (GF) homology groups. These GF-based capacities provide a
 lternate proofs of non-squeezing in their respective settings\, results or
 iginally due to Gromov and Eliashberg-Kim-Polterovich (EKP) respectively. 
 While Gromov proved the ball $B(R)$ cannot be squeezed into a narrower cyl
 inder\, the contact analog that EKP considered in $R^{2n} imes S^1$\, name
 ly squeezing of a pre-quantized ball $B(R) imes S^1$ into itself\, was rul
 ed out by EKP only for integer R while they showed squeezing actually hold
 s for R<1. Non-squeezing via a contact isotopy for all R>1 was established
  by Chiu (2014) using sheaf theory. I will describe a low-tech proof of th
 is result using analogs of Viterbo-Sandon capacities. I first introduce fi
 ltration-decreasing morphisms between GF homology groups that set up a fun
 ctor from a sub-category of $calD imes Z$ to Vect\, where $calD$ is the ca
 tegory of bounded domains with inclusion. Persistences in this persistence
  module then yield a sequence of integer-valued contact invariants for pre
 -quantized balls which rule out squeezing. \n
DTSTART:20161104T150000Z
DTEND:20161104T160000Z
LOCATION:PK-5115\, CA\, Pavillon Président-Kennedy
SUMMARY:Maia Fraser\, Université d'Ottawa
URL:/mathstat/channels/event/maia-fraser-universite-do
 ttawa-263862
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