This book consists of a selection of articles devoted to new ideas
and developments in low dimensional topology. Low dimensions refer
to dimensions three and four for the topology of manifolds and
their submanifolds. Thus we have papers related to both manifolds
and to knotted submanifolds of dimension one in three (classical
knot theory) and two in four (surfaces in four dimensional spaces).
Some of the work involves virtual knot theory where the knots are
abstractions of classical knots but can be represented by knots
embedded in surfaces. This leads both to new interactions with
classical topology and to new interactions with essential
combinatorics.
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