Ada94

# The knot book

W. H. Freeman & Co. 1994 Ago11

## Ideal triangulations of pseudo-Anosov mapping tori

Topology and Geometry in Dimension Three vol. 560 of Contemp. Math. pp. 1–17 Amer. Math. Soc.

    Providence, RI

2011 BB22

## Embeddings of 3-manifolds in `S` 4 from the point of view of the 11-tetrahedron census

Experimental Math. vol. 31 no. 3 pp. 988–1013 2022 Bur03

## Minimal triangulations and normal surfaces

PhD Thesis University of Melbourne May 2003 Available from the ®website; Bur04

## Face pairing graphs and 3-manifold enumeration

J. Knot Theory Ramifications vol. 13 no. 8 pp. 1057–1101 2004 Bur07a

## Enumeration of non-orientable 3-manifolds using face-pairing graphs and union-find

Discrete Comput. Geom. vol. 38 no. 3 pp. 527–571 2007 Bur07b

## Observations from the 8-tetrahedron nonorientable census

Experiment. Math. vol. 16 no. 2 pp. 129–144 2007 Bur07c

## Structures of small closed non-orientable 3-manifold triangulations

J. Knot Theory Ramifications vol. 16 no. 5 pp. 545–574 2007 Bur08a

## Building minimal triangulations of graph manifolds using saturated blocks

In preparation 2008 Bur09a

## Converting between quadrilateral and standard solution sets in normal surface theory

Algebr. Geom. Topol. vol. 9 no. 4 pp. 2121–2174 2009 Bur10a

## Optimizing the double description method for normal surface enumeration

Math. Comp. vol. 79 no. 269 pp. 453–484 2010 Bur10b

## Quadrilateral-octagon coordinates for almost normal surfaces

Experiment. Math. vol. 19 no. 3 pp. 285–315 2010 Bur11a

## Detecting genus in vertex links for the fast enumeration of 3-manifold triangulations

ISSAC 2011: Proceedings of the 36th International Symposium on Symbolic and Algebraic Computation pp. 59–66 ACM 2011 Bur11b

## The Pachner graph and the simplification of 3-sphere triangulations

SCG '11: Proceedings of the Twenty-Seventh Annual Symposium on Computational Geometry pp. 153–162 ACM 2011 Bur11c

## Simplification paths in the Pachner graphs of closed orientable 3-manifold triangulations

Preprint arXiv:1110.6080 October 2011 Bur13

## Computational topology with Regina: Algorithms, heuristics and implementations

Geometry and Topology Down Under vol. 597 of Contemp. Math. pp. 195–224 Amer. Math. Soc.

    Providence, RI

2013 Bur14a

## Enumerating fundamental normal surfaces: Algorithms, experiments and invariants

ALENEX 2014: Proceedings of the Meeting on Algorithm Engineering & Experiments pp. 112–124 SIAM 2014 Bur14b

## A new approach to crushing 3-manifold triangulations

Discrete Comput. Geom. vol. 52 no. 1 pp. 116–139 2014 Bur14c

## The cusped hyperbolic census is complete

Preprint arXiv:1405.2695 May 2014 Bur18

## The HOMFLY-PT polynomial is fixed-parameter tractable

34th International Symposium on Computational Geometry (SoCG 2018) vol. 99 of Leibniz Int. Proc. Inform. pp. 18:1–18:14 Schloss Dagstuhl – Leibniz-Zentrum fuer Informatik

    Dagstuhl, Germany

2018 Bur20

## The next 350 million knots

36th International Symposium on Computational Geometry (SoCG 2020) vol. 164 of Leibniz Int. Proc. Inform. pp. 25:1–25:17 Schloss Dagstuhl – Leibniz-Zentrum fuer Informatik

    Dagstuhl, Germany

2020 BCT13

## Computing closed essential surfaces in knot complements

SCG '13: Proceedings of the 29th Annual Symposium on Computational Geometry pp. 405–414 ACM 2013 BMS15

## Algorithms and complexity for Turaev-Viro invariants

ICALP 2015: Automata, Languages, and Programming: 42nd International Colloquium vol. 9134 of Lecture Notes in Comput. Sci. pp. 281–293 Springer 2015 BO12

## A fast branching algorithm for unknot recognition with experimental polynomial-time behaviour

Preprint arXiv:1211.1079 November 2012 BO13

## A tree traversal algorithm for decision problems in knot theory and 3-manifold topology

Algorithmica vol. 65 no. 4 pp. 772–801 2013 BRT12

## The Weber-Seifert dodecahedral space is non-Haken

Trans. Amer. Math. Soc. 364 2 pp. 911–932 2012 CHW99

## A census of cusped hyperbolic 3-manifolds

Math. Comp. vol. 68 no. 225 pp. 321–332 1999 CT09

## The Thurston norm via normal surfaces

Pacific J. Math. vol. 239 pp. 1–15 2009 FG11

## From angled triangulations to hyperbolic structures

Interactions Between Hyperbolic Geometry, Quantum Topology and Number Theory vol. 541 of Contemp. Math. pp. 159–182 Amer. Math. Soc.

    Providence, RI

2011 GAP02 The GAP Group

## GAP — Groups, Algorithms and Programming

Version 4.3 2002 Available from Hak62

## Über das Homöomorphieproblem der 3-Mannigfaltigkeiten. I

Math. Z. vol. 80 pp. 89–120 1962 Har20

## Determining hyperbolicity of compact orientable 3-manifolds with torus boundary

J. Comput. Geom. vol. 11 no. 1 pp. 125–136 2020 HLP99

## The computational complexity of knot and link problems

J. Assoc. Comput. Mach. vol. 46 no. 2 pp. 185–211 1999 HRST11

## Veering triangulations admit strict angle structures

Geom. Topol. vol. 15 no. 4 pp. 2073–2089 2011 HW94

## Symmetries, isometries and length spectra of closed hyperbolic three-manifolds

Experiment. Math. vol. 3 no. 4 pp. 261–274 1994 JO84

## An algorithm to decide if a 3-manifold is a Haken manifold

Topology vol. 23 no. 2 pp. 195–209 1984 JR03

## 0-efficient triangulations of 3-manifolds

J. Differential Geom. vol. 65 no. 1 pp. 61–168 2003 JR06

## Layered-triangulations of 3-manifolds

Preprint February 2006 KR05

## Ideal triangulations of 3-manifolds II; Taut and angle structures

Algebr. Geom. Topol. vol. 5 pp. 1505–1533 2005 Kau99

## Virtual knot theory

European J. Combin. vol. 20 no. 7 pp. 663–690 1999 KK80

## Algebraic classification of linking pairings on 3-manifolds

Math. Ann. vol. 253 no. 1 pp. 29–42 1980 Lac00a

## Taut ideal triangulations of 3-manifolds

Geom. Topol. vol. 4 pp. 369–395 (electronic) 2000 Lac00b

## Word hyperbolic Dehn surgery

Invent. Math. vol. 140 no. 2 pp. 243–282 2000 MP01

## Three-manifolds having complexity at most 9

Experiment. Math. vol. 10 no. 2 pp. 207–236 2001 Mat98

## Tables of 3-manifolds up to complexity 6

Max-Planck-Institut für Mathematik Preprint Series vol. 67 1998 Available from Riv94

## Euclidean structures on simplicial surfaces and hyperbolic volume

Ann. of Math. (2) vol. 139 no. 3 pp. 553–580 1994 Riv03

## Combinatorial optimization in geometry

Adv. in Appl. Math. vol. 31 no. 1 pp. 242–271 2003 Rub95

## An algorithm to recognize the 3-sphere

Proceedings of the International Congress of Mathematicians (Zürich, 1994) vol. 1 pp. 601–611 Birkhäuser

    Basel

1995 Rub97

## Polyhedral minimal surfaces, Heegaard splittings and decision problems for 3-dimensional manifolds

Geometric Topology (Athens, GA, 1993) vol. 2 of AMS/IP Stud. Adv. Math. pp. 1–20 Amer. Math. Soc.

    Providence, RI

1997 SW06

## Crowell's derived group and twisted polynomials

J. Knot Theory Ramifications vol. 15 no. 8 pp. 1079–1094 2006 Tho94

## Thin position and the recognition problem for S3

Math. Res. Lett. vol. 1 no. 5 pp. 613–630 1994 Til08

## Normal surfaces in topologically finite 3-manifolds

Enseign. Math. (2) vol. 54 pp. 329–380 2008 Tol98

## Normal surface `Q`-theory

Pacific J. Math. vol. 183 no. 2 pp. 359–374 1998 TV92

## State sum invariants of 3-manifolds and quantum 6`j`-symbols

Topology vol. 31 no. 4 pp. 865–902 1992 Wee93

## Convex hulls and isometries of cusped hyperbolic 3-manifolds

Topology Appl. vol. 52 pp. 127–149 1993