  It is natural to try to place the new polynomial invariants of links in
algebraic topology (e.g. to try to interpret them using homology or homotopy
groups). However, one can think that these new polynomial invariants are
byproducts of a new more delicate algebraic invariant of 3-manifolds which
measures the obstruction to isotopy of links (which are homotopic). We propose
such an algebraic invariant based on skein theory introduced by Conway (1969)
and developed by Giller (1982) as well as Lickorish and Millett (1987). (This
is the first paper I wrote about skein modules, almost 20 years ago. The recent
survey of skein modules is available at http://arxiv.org/abs/math.GT/0602264.)
