Algebraic & Geometric Topology Volume 19, issue 5 (2019)

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the Journal

Editorial Board

Subscriptions

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN 1472-2739 (online)

ISSN 1472-2747 (print)

Author Index

To Appear

Other MSP Journals

Treewidth, crushing and hyperbolic volume

Clément Maria and Jessica S Purcell

Algebraic & Geometric Topology 19 (2019) 2625–2652

DOI: 10.2140/agt.2019.19.2625

Bibliography

1	I Agol, Small 3–manifolds of large genus, Geom. Dedicata 102 (2003) 53 MR2026837
2	S Arnborg, D G Corneil, A Proskurowski, Complexity of finding embeddings in a k–tree, SIAM J. Algebraic Discrete Methods 8 (1987) 277 MR881187
3	S Arnborg, A Proskurowski, D G Corneil, Forbidden minors characterization of partial 3–trees, Discrete Math. 80 (1990) 1 MR1045920
4	R Benedetti, C Petronio, Lectures on hyperbolic geometry, Springer (1992) MR1219310
5	D Bienstock, On embedding graphs in trees, J. Combin. Theory Ser. B 49 (1990) 103 MR1056822
6	H L Bodlaender, A linear-time algorithm for finding tree-decompositions of small treewidth, SIAM J. Comput. 25 (1996) 1305 MR1417901
7	G Burde, H Zieschang, Knots, 5, de Gruyter (1985) MR808776
8	B A Burton, Introducing Regina, the 3–manifold topology software, Experiment. Math. 13 (2004) 267 MR2103324
9	B A Burton, A new approach to crushing 3–manifold triangulations, Discrete Comput. Geom. 52 (2014) 116 MR3231034
10	B A Burton, R G Downey, Courcelle’s theorem for triangulations, J. Combin. Theory Ser. A 146 (2017) 264 MR3574232
11	B A Burton, C Maria, J Spreer, Algorithms and complexity for Turaev–Viro invariants, from: "Automata, languages, and programming, I" (editors M M Halldórsson, K Iwama, N Kobayashi, B Speckmann), Lecture Notes in Comput. Sci. 9134, Springer (2015) 281 MR3382513
12	B A Burton, J Spreer, The complexity of detecting taut angle structures on triangulations, from: "Proceedings of the Twenty-Fourth Annual ACM–SIAM Symposium on Discrete Algorithms" (editor S Khanna), SIAM (2012) 168 MR3185388
13	B Courcelle, The monadic second-order logic of graphs, I : Recognizable sets of finite graphs, Inform. and Comput. 85 (1990) 12 MR1042649
14	M Culler, N Dunfield, M Goerner, J Weeks, SnapPy : a computer program for studying the geometry and topology of 3–manifolds, software (2016)
15	H Edelsbrunner, Geometry and topology for mesh generation, 7, Cambridge Univ. Press (2001) MR1833977
16	W Fenchel, Elementary geometry in hyperbolic space, 11, de Gruyter (1989) MR1004006
17	D Futer, E Kalfagianni, J S Purcell, Dehn filling, volume, and the Jones polynomial, J. Differential Geom. 78 (2008) 429 MR2396249
18	F Guéritaud, On canonical triangulations of once-punctured torus bundles and two-bridge link complements, Geom. Topol. 10 (2006) 1239 MR2255497
19	K Huszár, J Spreer, U Wagner, On the treewidth of triangulated 3–manifolds, from: "34th International Symposium on Computational Geometry" (editors B Speckmann, C D Tóth), Leibniz Int. Proc. Inform. 99, Schloss Dagstuhl. Leibniz-Zent. Inform. (2018) MR3824290
20	W Jaco, J H Rubinstein, 0–efficient triangulations of 3–manifolds, J. Differential Geom. 65 (2003) 61 MR2057531
21	W Jaco, J H Rubinstein, Layered-triangulations of 3–manifolds, preprint (2006) arXiv:math/0603601
22	W Jaco, E Sedgwick, Decision problems in the space of Dehn fillings, Topology 42 (2003) 845 MR1958532
23	D A Každan, G A Margulis, A proof of Selberg’s hypothesis, Mat. Sb. 75 (117) (1968) 163 MR0223487
24	B Kleiner, J Lott, Notes on Perelman’s papers, Geom. Topol. 12 (2008) 2587 MR2460872
25	T Kobayashi, Y Rieck, A linear bound on the tetrahedral number of manifolds of bounded volume (after Jørgensen and Thurston), from: "Topology and geometry in dimension three" (editors W Li, L Bartolini, J Johnson, F Luo, R Myers, J H Rubinstein), Contemp. Math. 560, Amer. Math. Soc. (2011) 27 MR2866921
26	C Maria, J Spreer, A polynomial time algorithm to compute quantum invariants of 3–manifolds with bounded first Betti number, from: "Proceedings of the Twenty-Eighth Annual ACM–SIAM Symposium on Discrete Algorithms" (editor P N Klein), SIAM (2017) 2721 MR3627909
27	G D Mostow, Strong rigidity of locally symmetric spaces, 78, Princeton Univ. Press (1973) MR0385004
28	G Perelman, The entropy formula for the Ricci flow and its geometric applications, preprint (2002) arXiv:math/0211159
29	G Perelman, Ricci flow with surgery on three-manifolds, preprint (2003) arXiv:math/0303109
30	J Purcell, Hyperbolic knot theory, book project (2018)
31	N Robertson, P D Seymour, Graph minors, II : Algorithmic aspects of tree-width, J. Algorithms 7 (1986) 309 MR855559
32	M Sakuma, J Weeks, Examples of canonical decompositions of hyperbolic link complements, Japan. J. Math. 21 (1995) 393 MR1364387
33	A Satyanarayana, L Tung, A characterization of partial 3–trees, Networks 20 (1990) 299 MR1050503
34	P D Seymour, R Thomas, Call routing and the ratcatcher, Combinatorica 14 (1994) 217 MR1289074
35	D M Thilikos, M J Serna, H L Bodlaender, Constructive linear time algorithms for small cutwidth and carving-width, from: "Algorithms and computation" (editors D T Lee, S H Teng), Lecture Notes in Comput. Sci. 1969, Springer (2000) 192 MR1858364
36	W P Thurston, The geometry and topology of three-manifolds, lecture notes (1979)