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

Volume 25, 1 issue

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
The upsilon invariant at $1$ of $3$–braid knots

Paula Truöl

Algebraic & Geometric Topology 23 (2023) 3763–3804
Bibliography
1 T Abe, An estimation of the alternation number of a torus knot, J. Knot Theory Ramifications 18 (2009) 363 MR2514849
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, 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
4 J W I Alexander, A lemma on systems of knotted curves, Proc. Natl. Acad. Sci. USA 9 (1923) 93
5 E Artin, Theorie der Zöpfe, Abh. Math. Sem. Univ. Hamburg 4 (1925) 47 MR3069440
6 S Baader, Positive braids of maximal signature, Enseign. Math. 59 (2013) 351 MR3189041
7 J A Baldwin, Heegaard Floer homology and genus one, one-boundary component open books, J. Topol. 1 (2008) 963 MR2461862
8 W Ballinger, Concordance invariants from the E(1) spectral sequence on Khovanov homology, preprint (2020) arXiv:2004.10807
9 D Bennequin, Entrelacements et équations de Pfaff, from: "Third Schnepfenried geometry conference, I", Astérisque 107–108, Soc. Math. France (1983) 87 MR0753131
10 J S Birman, T E Brendle, Braids: A survey, from: "Handbook of knot theory" (editors W Menasco, M Thistlethwaite), Elsevier (2005) 19 MR2179260
11 J S Birman, W W Menasco, Studying links via closed braids, III : Classifying links which are closed 3–braids, Pacific J. Math. 161 (1993) 25 MR1237139
12 M Brandenbursky, On quasi-morphisms from knot and braid invariants, J. Knot Theory Ramifications 20 (2011) 1397 MR2851716
13 A Champanerkar, I Kofman, A survey on the Turaev genus of knots, Acta Math. Vietnam. 39 (2014) 497 MR3292579
14 W L Chow, On the algebraical braid group, Ann. of Math. 49 (1948) 654 MR0026050
15 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
16 O T Dasbach, A M Lowrance, Turaev genus, knot signature, and the knot homology concordance invariants, Proc. Amer. Math. Soc. 139 (2011) 2631 MR2784832
17 D Erle, Calculation of the signature of a 3–braid link, Kobe J. Math. 16 (1999) 161 MR1745024
18 P Feller, Optimal cobordisms between torus knots, Comm. Anal. Geom. 24 (2016) 993 MR3622312
19 P Feller, D Hubbard, Braids with as many full twists as strands realize the braid index, J. Topol. 12 (2019) 1069 MR3977871
20 P Feller, D Krcatovich, On cobordisms between knots, braid index, and the upsilon-invariant, Math. Ann. 369 (2017) 301 MR3694648
21 P Feller, L Lewark, A Lobb, Squeezed knots, preprint (2022) arXiv:2202.12289
22 P Feller, S Pohlmann, R Zentner, Alternation numbers of torus knots with small braid index, Indiana Univ. Math. J. 67 (2018) 645 MR3798852
23 S Friedl, C Livingston, R Zentner, Knot concordances and alternating knots, Michigan Math. J. 66 (2017) 421 MR3657225
24 D Gabai, U Oertel, Essential laminations in 3–manifolds, Ann. of Math. 130 (1989) 41 MR1005607
25 F A Garside, The braid group and other groups, Quart. J. Math. Oxford Ser. 20 (1969) 235 MR0248801
26 R E Goodrick, Two bridge knots are alternating knots, Pacific J. Math. 40 (1972) 561 MR0315693
27 J E Greene, Donaldson’s theorem, Heegaard Floer homology, and knots with unknotting number one, Adv. Math. 255 (2014) 672 MR3167496
28 J Hom, A survey on Heegaard Floer homology and concordance, J. Knot Theory Ramifications 26 (2017) 1740015 MR3604497
29 D Hubbard, K Kawamuro, F C Kose, G Martin, O Plamenevskaya, K Raoux, L Truong, H Turner, Braids, fibered knots, and concordance questions, from: "Research directions in symplectic and contact geometry and topology" (editors B Acu, C Cannizzo, D McDuff, Z Myer, Y Pan, L Traynor), Assoc. Women Math. Ser. 27, Springer (2021) 293 MR4417720
30 T Kanenobu, Upper bound for the alternation number of a torus knot, Topology Appl. 157 (2010) 302 MR2556109
31 A Kawauchi, On alternation numbers of links, Topology Appl. 157 (2010) 274 MR2556105
32 P B Kronheimer, T S Mrowka, Gauge theory for embedded surfaces, I, Topology 32 (1993) 773 MR1241873
33 L Lewark, Rasmussen’s spectral sequences and the 𝔰𝔩N–concordance invariants, Adv. Math. 260 (2014) 59 MR3209349
34 C Livingston, Computations of the Ozsváth–Szabó knot concordance invariant, Geom. Topol. 8 (2004) 735 MR2057779
35 C Livingston, Notes on the knot concordance invariant upsilon, Algebr. Geom. Topol. 17 (2017) 111 MR3604374
36 C Livingston, A H Moore, KnotInfo: table of knot invariants, online resource (2021)
37 A Lowrance, The Khovanov width of twisted links and closed 3–braids, Comment. Math. Helv. 86 (2011) 675 MR2803857
38 A M Lowrance, Alternating distances of knots and links, Topology Appl. 182 (2015) 53 MR3305610
39 A V Malyutin, Writhe of (closed) braids, Algebra i Analiz 16 (2004) 59 MR2106667
40 C Manolescu, P Ozsváth, On the Khovanov and knot Floer homologies of quasi-alternating links, from: "Proceedings of the 14th Gökova geometry-topology conference" (editors S Akbulut, T Önder, R J Stern), GGT (2008) 60 MR2509750
41 G Martin, Annular Rasmussen invariants : Properties and 3–braid classification, preprint (2019) arXiv:1909.09245
42 H R Morton, Closed braids which are not prime knots, Math. Proc. Cambridge Philos. Soc. 86 (1979) 421 MR0542687
43 H Murakami, Some metrics on classical knots, Math. Ann. 270 (1985) 35 MR0769605
44 K Murasugi, On a certain numerical invariant of link types, Trans. Amer. Math. Soc. 117 (1965) 387 MR0171275
45 K Murasugi, On closed 3–braids, 151, Amer. Math. Soc. (1974) MR0356023
46 P S Ozsváth, A I Stipsicz, Z Szabó, Concordance homomorphisms from knot Floer homology, Adv. Math. 315 (2017) 366 MR3667589
47 P S Ozsváth, A I Stipsicz, Z Szabó, Unoriented knot Floer homology and the unoriented four-ball genus, Int. Math. Res. Not. 2017 (2017) 5137 MR3694597
48 P Ozsváth, Z Szabó, Knot Floer homology and the four-ball genus, Geom. Topol. 7 (2003) 615 MR2026543
49 J A Rasmussen, Floer homology and knot complements, PhD thesis, Harvard University (2003) arXiv:math/0306378 MR2704683
50 J Rasmussen, Khovanov homology and the slice genus, Invent. Math. 182 (2010) 419 MR2729272
51 L Rudolph, Quasipositivity as an obstruction to sliceness, Bull. Amer. Math. Soc. 29 (1993) 51 MR1193540
52 O Schreier, Über die gruppen AaBb = 1, Abh. Math. Sem. Univ. Hamburg 3 (1924) 167 MR3069424
53 T Shibuya, Some relations among various numerical invariants for links, Osaka Math. J. 11 (1974) 313 MR0353295
54 H F Trotter, Homology of group systems with applications to knot theory, Ann. of Math. 76 (1962) 464 MR0143201