Algebraic & Geometric Topology Volume 13, issue 5 (2013)

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

A classification of spanning surfaces for alternating links

Colin Adams and Thomas Kindred

Algebraic & Geometric Topology 13 (2013) 2967–3007

DOI: 10.2140/agt.2013.13.2967

Bibliography

1	C C Adams, The knot book: An elementary introduction to the mathematical theory of knots, W. H. Freeman (1994) MR1266837
2	C C Adams, Toroidally alternating knots and links, Topology 33 (1994) 353 MR1273788
3	C Adams, Noncompact Fuchsian and quasi-Fuchsian surfaces in hyperbolic $3$–manifolds, Algebr. Geom. Topol. 7 (2007) 565 MR2308957
4	C C Adams, J F Brock, J Bugbee, e al., Almost alternating links, Topology Appl. 46 (1992) 151 MR1184114
5	C Adams, R Dorman, K Foley, J Kravis, S Payne, Alternating graphs, J. Combin. Theory Ser. B 77 (1999) 96 MR1710534
6	C Adams, T Fleming, M Levin, A M Turner, Crossing number of alternating knots in $S\times I$, Pacific J. Math. 203 (2002) 1 MR1895923
7	B A Burton, M Ozlen, Computing the crosscap number of a knot using integer programming and normal surfaces, ACM Trans. Math. Software 39 (2012) 18 MR3002773
8	B E Clark, Crosscaps and knots, Internat. J. Math. Math. Sci. 1 (1978) 113 MR0478131
9	R Crowell, Genus of alternating link types, Ann. of Math. 69 (1959) 258 MR0099665
10	C L Curtis, S J Taylor, The Jones polynomial and boundary slopes of alternating knots, J. Knot Theory Ramifications 20 (2011) 1345 MR2851712
11	D Futer, Fiber detection for state surfaces arXiv:1201.1643
12	D Futer, E Kalfagianni, J S Purcell, Quasifuchsian state surfaces arXiv:1209.5719
13	D Futer, E Kalfagianni, J Purcell, Guts of surfaces and the colored Jones polynomial, Lecture Notes in Mathematics 2069, Springer (2013) MR3024600
14	D Gabai, Genera of the alternating links, Duke Math. J. 53 (1986) 677 MR860665
15	A Hatcher, W Thurston, Incompressible surfaces in $2$–bridge knot complements, Invent. Math. 79 (1985) 225 MR778125
16	C Hayashi, Links with alternating diagrams on closed surfaces of positive genus, Math. Proc. Cambridge Philos. Soc. 117 (1995) 113 MR1297898
17	M Hirasawa, M Teragaito, Crosscap numbers of $2$–bridge knots, Topology 45 (2006) 513 MR2218754
18	J Hoste, M Thistlethwaite, J Weeks, The first 1,701,936 knots, Math. Intelligencer 20 (1998) 33 MR1646740
19	K Ichihara, S Mizushima, Crosscap numbers of pretzel knots, Topology Appl. 157 (2010) 193 MR2556097
20	T W Mattman, O Sizemore, Bounds on the crosscap number of torus knots, J. Knot Theory Ramifications 16 (2007) 1043 MR2364888
21	W Menasco, Closed incompressible surfaces in alternating knot and link complements, Topology 23 (1984) 37 MR721450
22	W Menasco, M Thistlethwaite, A geometric proof that alternating knots are nontrivial, Math. Proc. Cambridge Philos. Soc. 109 (1991) 425 MR1094743
23	W W Menasco, M B Thistlethwaite, The Tait flyping conjecture, Bull. Amer. Math. Soc. 25 (1991) 403 MR1098346
24	W W Menasco, M B Thistlethwaite, Surfaces with boundary in alternating knot exteriors, J. Reine Angew. Math. 426 (1992) 47 MR1155746
25	W Menasco, M Thistlethwaite, The classification of alternating links, Ann. of Math. 138 (1993) 113 MR1230928
26	Y Mizuma, Y Tsutsumi, Crosscap number, ribbon number and essential tangle decompositions of knots, Osaka J. Math. 45 (2008) 391 MR2441946
27	H Murakami, A Yasuhara, Crosscap number of a knot, Pacific J. Math. 171 (1995) 261 MR1362987
28	K Murasugi, On the genus of the alternating knot, I, J. Math. Soc. Japan 10 (1958) 94 MR0099664
29	K Murasugi, On the genus of the alternating knot, II, J. Math. Soc. Japan 10 (1958) 235 MR0099664
30	M Ozawa, Essential state surfaces for knots and links, J. Aust. Math. Soc. 91 (2011) 391 MR2900614
31	M D Pabiniak, J H Przytycki, R Sazdanović, On the first group of the chromatic cohomology of graphs, Geom. Dedicata 140 (2009) 19 MR2504733
32	S Rankin, O Flint, J Schermann, Enumerating the prime alternating knots, I, J. Knot Theory Ramifications 13 (2004) 57 MR2039118
33	S Rankin, O Flint, J Schermann, Enumerating the prime alternating knots, II, J. Knot Theory Ramifications 13 (2004) 101 MR2039119
34	M Teragaito, Crosscap numbers of torus knots, Topology Appl. 138 (2004) 219 MR2035482
35	C M Tsau, A note on incompressible surfaces in solid tori and in lens spaces, from: "Knots 90" (editor A Kawauchi), de Gruyter (1992) 213 MR1177425
36	T Tsukamoto, A criterion for almost alternating links to be non-splittable, Math. Proc. Cambridge Philos. Soc. 137 (2004) 109 MR2075045
37	G Zhang, Crosscap numbers of two-component links, Kyungpook Math. J. 48 (2008) 241 MR2429312