Last Updated：2025/12/31
Sentence
In
this
expository
article
I
will
review
some
constructions
of
bi-invariant
metrics
on
the
contactomorphism
group,
and
how
these
metrics
are
related
to
some
other
global
rigidity
phenomena
in
contact
topology
which
have
been
discovered
in
the
last
few
years,
in
particular
the
notion
of
orderability
(due
to
Eliashberg
and
Polterovich)
and
an
analogue
in
contact
topology
(due
to
Eliashberg,
Kim
and
Poltorovich)
of
Gromov's
symplectic
non-squeezing
theorem..
Quizzes for review
In this expository article I will review some constructions of bi-invariant metrics on the contactomorphism group, and how these metrics are related to some other global rigidity phenomena in contact topology which have been discovered in the last few years, in particular the notion of orderability (due to Eliashberg and Polterovich) and an analogue in contact topology (due to Eliashberg, Kim and Poltorovich) of Gromov's symplectic non-squeezing theorem..
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