Volume 20, issue 3 (2016)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 23
Issue 3, 1085–1619
Issue 2, 541–1084
Issue 1, 1–540

Volume 22, 7 issues

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Subscriptions
Editorial Board
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Ethics Statement
Author Index
To Appear
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Other MSP Journals
Bounds for the genus of a normal surface

William Jaco, Jesse Johnson, Jonathan Spreer and Stephan Tillmann

Geometry & Topology 20 (2016) 1625–1671
Bibliography
1 A Altshuler, Polyhedral realization in R3 of triangulations of the torus and 2–manifolds in cyclic 4–polytopes, Discrete Math. 1 (1971/1972) 211 MR0287431
2 A Altshuler, Combinatorial 3–manifolds with few vertices, J. Combinatorial Theory Ser. A 16 (1974) 165 MR0346797
3 D Archdeacon, C P Bonnington, J A Ellis-Monaghan, How to exhibit toroidal maps in space, Discrete Comput. Geom. 38 (2007) 573 MR2352708
4 J Bokowski, On heuristic methods for finding realizations of surfaces, from: "Discrete differential geometry" (editors A I Bobenko, P Schröder, J M Sullivan, G M Ziegler), Oberwolfach Semin. 38, Birkhäuser (2008) 255 MR2405670
5 J Bokowski, U Brehm, A new polyhedron of genus 3 with 10 vertices, from: "Intuitive geometry" (editors K Böröczky, G Fejes Tóth), Colloq. Math. Soc. János Bolyai 48, North-Holland (1987) 105 MR910704
6 J Bokowski, A Eggert, Toutes les réalisations du tore de Möbius avec sept sommets, Structural Topology (1991) 59 MR1140405
7 M Bucher, R Frigerio, C Pagliantini, The simplicial volume of 3–manifolds with boundary, J. Topol. 8 (2015) 457 MR3356768
8 B A Burton, Face pairing graphs and 3–manifold enumeration, J. Knot Theory Ramifications 13 (2004) 1057 MR2108649
9 B A Burton, Enumeration of non-orientable 3–manifolds using face-pairing graphs and union-find, Discrete Comput. Geom. 38 (2007) 527 MR2352707
10 B A Burton, R Budney, W Petterson, Regina : Software for 3–manifold topology and normal surface theory
11 B A Burton, A Coward, S Tillmann, Computing closed essential surfaces in knot complements, from: "Computational geometry", ACM (2013) 405 MR3208239
12 B A Burton, M Ozlen, A tree traversal algorithm for decision problems in knot theory and 3–manifold topology, Algorithmica 65 (2013) 772 MR3018150
13 B A Burton, J Paixão, J Spreer, Computational Topology and Normal Surfaces: Theoretical and Experimental Complexity Bounds, from: "Proceedings of the Meeting on Algorithm Engineering & Expermiments", SIAM (2013) 78
14 D Cooper, S Tillmann, The Thurston norm via normal surfaces, Pacific J. Math. 239 (2009) 1 MR2449008
15 Á Császár, A polyhedron without diagonals, Acta Univ. Szeged. Sect. Sci. Math. 13 (1949) 140 MR0035029
16 R A Duke, Geometric embedding of complexes, Amer. Math. Monthly 77 (1970) 597 MR0264670
17 F Effenberger, J Spreer, simpcomp
18 R Frigerio, B Martelli, C Petronio, Complexity and Heegaard genus of an infinite class of compact 3–manifolds, Pacific J. Math. 210 (2003) 283 MR1988535
19 B Grünbaum, Convex polytopes, 221, Springer (2003) MR1976856
20 W Haken, Theorie der Normalflächen, Acta Math. 105 (1961) 245 MR0141106
21 W Haken, Über das Homöomorphieproblem der 3–Mannigfaltigkeiten, I, Math. Z. 80 (1962) 89 MR0160196
22 J Hass, J C Lagarias, N Pippenger, The computational complexity of knot and link problems, J. ACM 46 (1999) 185 MR1693203
23 G Hemion, On the classification of homeomorphisms of 2–manifolds and the classification of 3–manifolds, Acta Math. 142 (1979) 123 MR512214
24 S Hougardy, F H Lutz, M Zelke, Surface realization with the intersection segment functional, Experiment. Math. 19 (2010) 79 MR2649986
25 W Jaco, U Oertel, An algorithm to decide if a 3–manifold is a Haken manifold, Topology 23 (1984) 195 MR744850
26 W Jaco, H Rubinstein, S Tillmann, Minimal triangulations for an infinite family of lens spaces, J. Topol. 2 (2009) 157 MR2499441
27 W Jaco, J H Rubinstein, 0–efficient triangulations of 3–manifolds, J. Differential Geom. 65 (2003) 61 MR2057531
28 W Jaco, J H Rubinstein, Inflations of ideal triangulations, Adv. Math. 267 (2014) 176 MR3269178
29 W Jaco, J H Rubinstein, S Tillmann, Coverings and minimal triangulations of 3–manifolds, Algebr. Geom. Topol. 11 (2011) 1257 MR2801418
30 T Kalelkar, Euler characteristic and quadrilaterals of normal surfaces, Proc. Indian Acad. Sci. Math. Sci. 118 (2008) 227 MR2423235
31 H Kneser, Geschlossene Flächen in dreidimensionalen Mannigfaltigkeiten, Jahresber. Dtsch. Math.-Ver. 38 (1929) 248
32 F Luo, S Tillmann, A new combinatorial class of 3–manifold triangulations, preprint (2015) arXiv:1312.5087v2
33 F H Lutz, The Manifold Page, electronic resource
34 F H Lutz, Enumeration and random realization of triangulated surfaces, from: "Discrete differential geometry" (editors A I Bobenko, P Schröder, J M Sullivan, G M Ziegler), Oberwolfach Semin. 38, Birkhäuser (2008) 235 MR2405669
35 S V Matveev, Complexity theory of three-dimensional manifolds, Acta Appl. Math. 19 (1990) 101 MR1074221
36 S V Matveev, Algorithmic topology and classification of 3–manifolds, 9, Springer (2003) MR1997069
37 P McMullen, C Schulz, J M Wills, Polyhedral 2–manifolds in E3 with unusually large genus, Israel J. Math. 46 (1983) 127 MR727027
38 G Ringel, Map color theorem, 209, Springer (1974) MR0349461
39 J H Rubinstein, An algorithm to recognize the 3–sphere, from: "Proceedings of the International Congress of Mathematicians, Volume 1" (editor S D Chatterji), Birkhäuser (1995) 601 MR1403961
40 J H Rubinstein, Polyhedral minimal surfaces, Heegaard splittings and decision problems for 3–dimensional manifolds, from: "Geometric topology" (editor W H Kazez), AMS/IP Stud. Adv. Math. 2, Amer. Math. Soc. (1997) 1 MR1470718
41 L Schewe, Nonrealizable minimal vertex triangulations of surfaces: showing nonrealizability using oriented matroids and satisfiability solvers, Discrete Comput. Geom. 43 (2010) 289 MR2579697
42 J Spreer, Normal surfaces as combinatorial slicings, Discrete Math. 311 (2011) 1295 MR2795540
43 E Steinitz, Über die Eulerschen Polyederrelationen, Arch. der Math. u. Phys. 11 (1906) 86
44 A Thompson, Thin position and the recognition problem for S3, Math. Res. Lett. 1 (1994) 613 MR1295555
45 S Tillmann, Normal surfaces in topologically finite 3–manifolds, Enseign. Math. 54 (2008) 329 MR2478091
46 J L Tollefson, Normal surface Q–theory, Pacific J. Math. 183 (1998) 359 MR1625962
47 A Y Vesnin, E A Fominykh, Exact values of the complexity of Paoluzzi–Zimmermann manifolds, Dokl. Akad. Nauk 439 (2011) 727 MR2883799
48 G M Ziegler, Polyhedral surfaces of high genus, from: "Discrete differential geometry" (editors A I Bobenko, P Schröder, J M Sullivan, G M Ziegler), Oberwolfach Semin. 38, Birkhäuser (2008) 191 MR2405667