Invariants of link and knots on T-polyhedra
by
Pavel V. Svetlov
Russian State Pedagogical University, St. Petersburg

Any link in R^3 can be isotopically deformed to the polyhedron T obtained from three semiplanes by attaching along their boundary lines. Any link K in T canonically bounds an embedding (oriented or nonoriented) surface M_K in T. Arising nontrivial theory of links and knots on the T was developed in []. The founded family of invariants of colored links has a rich combinatorial characteristics permitting to construct isotopic invariants of (noncolored) links that can distinguish knots on T that are isotopic as knots in R^3. The results will be interpreted in a context of "cubic spaces", i.e. Goussarov's theory of invariants of a finite degree.

[] Svetlov P. Invariants of link and knots on T-polyhedra. Zap.Nauchn.Sem.POMI, vol.252, 1998.

Date received: August 11, 1999