The book is devoted to algorithmic low-dimensional topology. This branch of mathematics
has recently been undergoing an intense development. On the one hand, the exponential …

The paper presents a detailed survey of results concerning the main decision problems of
group theory and semigroup theory, including the word problem, the isomorphism problem …

This paper is the second in a series whose goal is to understand the structure of low-volume
complete orientable hyperbolic $3 $-manifolds. Using Mom technology, we prove that any …

We prove that the three-sphere recognition problem lies in NP. Rubinstein [Haifa, 1992] and
Thompson [Math. Res. Let., 1994] showed that the problem is decidable. Our result relies on …

JH Rubinstein introduced the theory of almost normal surfaces to solve several
homeomorphism problems for 3-manifolds. A. Thompson simplified Rubinstein's algorithm …

We present a fast enumeration algorithm for combinatorial 2-and 3-manifolds. In particular,
we enumerate all triangulated surfaces with 11 and 12 vertices and all triangulated 3 …

The paper presents a detailed survey of results concerning the main decision problems of
group theory and semigroup theory, including the word problem, the isomorphism problem …

arXiv:math/9712269v1 [math.GT] 30 Dec 1997 Page 1 arXiv:math/9712269v1 [math.GT] 30 Dec
1997 Algorithms for recognizing knots and 3-manifolds Joel Hass ∗ February 1, 2008 1 …

This paper introduces Mom technology to understand low volume hyperbolic 3-manifolds; it
is used in [GMM3] and [M1] to show that the Weeks manifold is the unique closed orientable …

We study the computational complexity of basic decision problems of 3-dimensional
topology, such as to determine whether a triangulated 3-manifold is irreducible, prime,∂ …