The theory of elementary moves on special polyhedra is elaborated. It is proved that the restriction of the Zeeman conjecture onto special polyhedra is equivalent to the union of the Poincare conjecture and the Andrews–Curtis conjecture. Complexity theory of 3-manifolds is constructed and all the manifolds up to complexity 8 are classified. A closed hyperbolic 3-manifold of the smallest complexity is constructed. It has the smallest known volume. A complete proof of the algorithmic classification theorem for sufficiently large 3-manifolds is written.
Main publications:
Matveev S., Rolfsen D. Spines and embeddings of $n$-manifolds // J. London Math. Soc. (2). V. 59. 1999. P. 359–368.
Matveev S. Computer classification of 3-manifolds // Russian Journal of Mathematical Physics. V. 7, no. 3. 2000. P. 319–329.
