Algorithmic Topology and Classification of 3-Manifolds

By S. Matveev. 2003

423 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computational Theory and Mathematics, Computer Vision and Pattern Recognition

View Paper: https://www.semanticscholar.org/paper/d1f6e14769794d27e25440fc07dad957e8f7154b

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Mechanics

1. H. Dye
2. T. Panov
3. Louis H. Kauffman
4. J. Lott
5. Bruce Kleiner
6. J. Greene
7. Marc Lackenby
8. V. Buchstaber

In Computational Theory and Mathematics

1. Marc Lackenby
2. J. Greene
3. V. Buchstaber
4. Louis H. Kauffman
5. T. Panov
6. J. Lott
7. H. Dye
8. Bruce Kleiner

In Computer Vision and Pattern Recognition

1. T. Panov
2. Louis H. Kauffman
3. J. Lott
4. H. Dye
5. Bruce Kleiner
6. J. Greene
7. Marc Lackenby
8. V. Buchstaber

Citations in the corpus

• Alternating links and definite surfaces (2015, background): “A much more complete survey can be found in the book of Matveev [Mat03].”
• Toric Topology (2012, background): “See detailed exposition in Matveev’s book [154], which also contains a proof that all 3-dimensional Haken manifolds can be recognised and fully classified algorithmically.”
• Notes on Perelman's papers (2006, background): “A reference for graph manifolds is [ 42, Chapter 2.4 ].”
• ESSENTIAL STATE SURFACES FOR KNOTS AND LINKS (2006, background): “For knot theory, graph theory and 3-manifold theory terminology, we refer to [5, 7, 17].”
• A polynomial upper bound on Reidemeister moves (2013, methodology): “This was finally solved by the efforts of several mathematicians, including Hemion [17] and Matveev [22].”
• Arc-presentations of links. Monotonic simplification (2002, methodology): “A solution published in [13] uses contributions of many mathematicians including W.”
• Quantum invariants of closed framed $3$-manifolds based on ideal triangulations (2022, background): “An oriented branching on an oriented standard polyhedron P is an orientation on connected components (2-cells) of D(P ) such that on each 1-cell, the orientations induced from the 2-cells attached to it are not 1In [20], standard spine is called special spine.”
• Dimensional reduction and the long-time behavior of Ricci flow (2007, background): “We now discuss graph manifolds. A reference is [ 39, Chapter 2.4 ].”
• Minimal surface representations of virtual knots and links (2004, background): “However, such algorithms can be formulated using normal surface theory [16], [18].”
• Geometrisation of 3-Manifolds (2010, neutral): “Matveev [Mat97], [Mat03].”
• Gauge Theories Labelled by Three-Manifolds (2011, neutral): “[21].”