Volume 17, issue 2 (2017)

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

Volume 25
Issue 3, 1265–1915
Issue 2, 645–1264
Issue 1, 1–644

Volume 24, 9 issues

Volume 23, 9 issues

Volume 22, 8 issues

Volume 21, 7 issues

Volume 20, 7 issues

Volume 19, 7 issues

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 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
Turaev genus and alternating decompositions

Cody W Armond and Adam M Lowrance

Algebraic & Geometric Topology 17 (2017) 793–830
Bibliography
1 T Abe, The Turaev genus of an adequate knot, Topology Appl. 156 (2009) 2704 MR2556029
2 T Abe, K Kishimoto, The dealternating number and the alternation number of a closed 3–braid, J. Knot Theory Ramifications 19 (2010) 1157 MR2726563
3 C C Adams, Toroidally alternating knots and links, Topology 33 (1994) 353 MR1273788
4 C C Adams, J F Brock, J Bugbee, T D Comar, K A Faigin, A M Huston, A M Joseph, D Pesikoff, Almost alternating links, Topology Appl. 46 (1992) 151 MR1184114
5 C Armond, N Druivenga, T Kindred, Heegaard diagrams corresponding to Turaev surfaces, J. Knot Theory Ramifications 24 (2015) 1 MR3346925
6 Y Bae, H R Morton, The spread and extreme terms of Jones polynomials, J. Knot Theory Ramifications 12 (2003) 359 MR1983092
7 C L J Balm, Topics in knot theory : on generalized crossing changes and the additivity of the Turaev genus, PhD thesis, Michigan State University (2013) MR3153295
8 A Champanerkar, I Kofman, Twisting quasi-alternating links, Proc. Amer. Math. Soc. 137 (2009) 2451 MR2495282
9 A Champanerkar, I Kofman, A survey on the Turaev genus of knots, Acta Math. Vietnam. 39 (2014) 497 MR3292579
10 A Champanerkar, I Kofman, N Stoltzfus, Graphs on surfaces and Khovanov homology, Algebr. Geom. Topol. 7 (2007) 1531 MR2366169
11 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
12 O T Dasbach, D Futer, E Kalfagianni, X S Lin, N W Stoltzfus, Alternating sum formulae for the determinant and other link invariants, J. Knot Theory Ramifications 19 (2010) 765 MR2665767
13 O T Dasbach, A M Lowrance, Turaev genus, knot signature, and the knot homology concordance invariants, Proc. Amer. Math. Soc. 139 (2011) 2631 MR2784832
14 O T Dasbach, A M Lowrance, A Turaev surface approach to Khovanov homology, Quantum Topol. 5 (2014) 425 MR3317340
15 O T Dasbach, A M Lowrance, Invariants for Turaev genus one links, preprint (2016) arXiv:1604.03501
16 J A Ellis-Monaghan, I Moffatt, Graphs on surfaces: dualities, polynomials, and knots, , Springer (2013) MR3086663
17 V F R Jones, A polynomial invariant for knots via von Neumann algebras, Bull. Amer. Math. Soc. 12 (1985) 103 MR766964
18 L H Kauffman, State models and the Jones polynomial, Topology 26 (1987) 395 MR899057
19 M Khovanov, A categorification of the Jones polynomial, Duke Math. J. 101 (2000) 359 MR1740682
20 M Khovanov, Patterns in knot cohomology, I, Experiment. Math. 12 (2003) 365 MR2034399
21 D Kim, J Lee, Some invariants of pretzel links, Bull. Austral. Math. Soc. 75 (2007) 253 MR2312569
22 S Kim, Link diagrams with low Turaev genus, preprint (2015) arXiv:1507.02918
23 A M Lowrance, On knot Floer width and Turaev genus, Algebr. Geom. Topol. 8 (2008) 1141 MR2443110
24 A Lowrance, The Khovanov width of twisted links and closed 3–braids, Comment. Math. Helv. 86 (2011) 675 MR2803857
25 A M Lowrance, Alternating distances of knots and links, Topology Appl. 182 (2015) 53 MR3305610
26 K Murasugi, Jones polynomials and classical conjectures in knot theory, Topology 26 (1987) 187 MR895570
27 P Ozsváth, Z Szabó, Knot Floer homology and the four-ball genus, Geom. Topol. 7 (2003) 615 MR2026543
28 P Ozsváth, Z Szabó, Holomorphic disks and knot invariants, Adv. Math. 186 (2004) 58 MR2065507
29 J A Rasmussen, Floer homology and knot complements, PhD thesis, Harvard University (2003) MR2704683
30 J Rasmussen, Khovanov homology and the slice genus, Invent. Math. 182 (2010) 419 MR2729272
31 M B Thistlethwaite, An upper bound for the breadth of the Jones polynomial, Math. Proc. Cambridge Philos. Soc. 103 (1988) 451 MR932668
32 V G Turaev, A simple proof of the Murasugi and Kauffman theorems on alternating links, Enseign. Math. 33 (1987) 203 MR925987