Algebraic & Geometric Topology Volume 20, issue 2 (2020)

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

State graphs and fibered state surfaces

Darlan Girão and Jessica S Purcell

Algebraic & Geometric Topology 20 (2020) 987–1014

DOI: 10.2140/agt.2020.20.987

Bibliography

1	P Bartholomew, S McQuarrie, J S Purcell, K Weser, Volume and geometry of homogeneously adequate knots, J. Knot Theory Ramifications 24 (2015) MR3383525
2	S D Burton, E Kalfagianni, Geometric estimates from spanning surfaces, Bull. Lond. Math. Soc. 49 (2017) 694 MR3725490
3	R H Crowell, H F Trotter, A class of pretzel knots, Duke Math. J. 30 (1963) 373 MR153006
4	O T Dasbach, D Futer, E Kalfagianni, X S Lin, N W Stoltzfus, The Jones polynomial and graphs on surfaces, J. Combin. Theory Ser. B 98 (2008) 384 MR2389605
5	K Finlinson, J S Purcell, Volumes of Montesinos links, Pacific J. Math. 282 (2016) 63 MR3463425
6	D Futer, Fiber detection for state surfaces, Algebr. Geom. Topol. 13 (2013) 2799 MR3116303
7	D Futer, E Kalfagianni, J Purcell, Guts of surfaces and the colored Jones polynomial, 2069, Springer (2013) MR3024600
8	D Futer, E Kalfagianni, J S Purcell, Quasifuchsian state surfaces, Trans. Amer. Math. Soc. 366 (2014) 4323 MR3206461
9	D Futer, E Kalfagianni, J S Purcell, Hyperbolic semi-adequate links, Comm. Anal. Geom. 23 (2015) 993 MR3458811
10	D Gabai, Detecting fibred links in S³, Comment. Math. Helv. 61 (1986) 519 MR870705
11	P Ghiggini, Knot Floer homology detects genus-one fibred knots, Amer. J. Math. 130 (2008) 1151 MR2450204
12	D Girão, On the fibration of augmented link complements, Geom. Dedicata 168 (2014) 207 MR3158039
13	D Girão, J Nogueira, A Salgueiro, Fiber surfaces from alternating states, Algebr. Geom. Topol. 15 (2015) 2805 MR3426693
14	S Goodman, G Tavares, Pretzel-fibered links, Bol. Soc. Brasil. Mat. 15 (1984) 85 MR794730
15	J Harer, How to construct all fibered knots and links, Topology 21 (1982) 263 MR649758
16	A Hatcher, W Thurston, Incompressible surfaces in 2–bridge knot complements, Invent. Math. 79 (1985) 225 MR778125
17	M Hirasawa, K Murasugi, Genera and fibredness of Montesinos knots, Pacific J. Math. 225 (2006) 53 MR2233725
18	E Kalfagianni, C R S Lee, On the degree of the colored Jones polynomial, Acta Math. Vietnam. 39 (2014) 549 MR3292583
19	T Kanenobu, The augmentation subgroup of a pretzel link, Math. Sem. Notes Kobe Univ. 7 (1979) 363 MR557309
20	I Kapovich, A Myasnikov, Stallings foldings and subgroups of free groups, J. Algebra 248 (2002) 608 MR1882114
21	L H Kauffman, State models and the Jones polynomial, Topology 26 (1987) 395 MR899057
22	K Murasugi, On a certain subgroup of the group of an alternating link, Amer. J. Math. 85 (1963) 544 MR157375
23	K Murasugi, Knot theory & its applications, Birkhäuser (2008) MR2347576
24	L Neuwirth, Knot groups, PhD thesis, Princeton University (1959) MR2612895
25	Y Ni, Knot Floer homology detects fibred knots, Invent. Math. 170 (2007) 577 MR2357503
26	M Ozawa, Essential state surfaces for knots and links, J. Aust. Math. Soc. 91 (2011) 391 MR2900614
27	M D Pabiniak, J H Przytycki, R Sazdanović, On the first group of the chromatic cohomology of graphs, Geom. Dedicata 140 (2009) 19 MR2504733
28	R L Parris, Pretzel knots, PhD thesis, Princeton University (1978) MR2628154
29	J Stallings, On fibering certain 3–manifolds, from: "Topology of 3–manifolds and related topics" (editor J M. K. Fort), Prentice-Hall (1962) 95 MR0158375
30	J R Stallings, Constructions of fibred knots and links, from: "Algebraic and geometric topology, II" (editor R J Milgram), Proc. Sympos. Pure Math. 32, Amer. Math. Soc. (1978) 55 MR520522
31	J R Stallings, Topology of finite graphs, Invent. Math. 71 (1983) 551 MR695906
32	N W M Touikan, A fast algorithm for Stallings’ folding process, Internat. J. Algebra Comput. 16 (2006) 1031 MR2286421