We describe the theoretical background for a computer program that recognizes all closed orientable three-manifolds up to complexity 8. The program can treat also nonclosed three-manifolds and manifolds of greater complexity, but without necessarily succeeding in recognizing them.
We establish two-sided bounds for the complexity of two infinite series of closed orientable 3-dimensional hyperbolic manifolds, the Löbell manifolds and the Fibonacci manifolds.
Cubic complexes appear in the theory of finite type invariants so often that one can ascribe them to basic notions of the theory. In this paper we begin the exposition of finite type invariants from the 'cubic' point of view. Finite type invariants of knots and homology 3-spheres fit perfectly into this conception. In particular, we get a natural… (More)
295 arXiv version: fonts, pagination and layout may vary from GTM published version Roots in 3–manifold topology C HOG-ANGELONI S MATVEEV Let C be some class of objects equipped with a set of simplifying moves. When we apply these to a given object M ∈ C as long as possible, we get a root of M. Our main result is that under certain conditions the root of… (More)
CONTENTS Let M and P be Seifert 3-manifolds. Is there a degree one map 1. Introduction f : M-> P ? The problem was completely solved by Hayat-2. A Bit of Theory Legrand, Wang, and Zieschang for all cases except when P is the 3. How to Calculate the Boundary Cycle Poincare homology sphere. We investigate the remaining case 4. How to Calculate the… (More)
We establish an existence and uniqueness theorem for prime decompositions of theta-curves in 3-manifolds.
Gauss diagram formulas are extensively used to study Vassiliev link invariants. Now we apply this approach to invariants of 3-manifolds, considering a manifold as a result M L of surgery on a framed link L in S 3. We study the lowest degree case – the celebrated Casson-Walker invariant λw of rational homology spheres. This paper is dedicated to a detailed… (More)
In this article we expose a proof of the Canonical Decomposition Theorem of irreducible 3-manifolds along tori and annuli, also known as JSJ Theorem. This proof will be based on the ideas that S. Matveev used in his article  which we extend from the closed to the compact case. The result is equivalent to the one proved by W.D. Neumann and G.A. Swarup in… (More)