Volume 13, issue 3 (2013)

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

Volume 24
Issue 2, 595–1223
Issue 1, 1–594

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
Editorial Interests
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Author Index
To Appear
Other MSP Journals
The classification of rational subtangle replacements between rational tangles

Kenneth L Baker and Dorothy Buck

Algebraic & Geometric Topology 13 (2013) 1413–1463
1 C Adams, Unknotting tunnels in hyperbolic $3$–manifolds, Math. Ann. 302 (1995) 177 MR1329452
2 C C Adams, A W Reid, Unknotting tunnels in two-bridge knot and link complements, Comment. Math. Helv. 71 (1996) 617 MR1420513
3 K L Baker, Surgery descriptions and volumes of Berge knots. I. Large volume Berge knots, J. Knot Theory Ramifications 17 (2008) 1077 MR2457837
4 K L Baker, Surgery descriptions and volumes of Berge knots. II. Descriptions on the minimally twisted five chain link, J. Knot Theory Ramifications 17 (2008) 1099 MR2457838
5 K L Baker, J E Grigsby, M Hedden, Grid diagrams for lens spaces and combinatorial knot Floer homology, Int. Math. Res. Not. 2008 (2008) 39 MR2429242
6 J Berge, Some knots with surgeries yielding lens spaces
7 J Berge, The knots in $D^2\times S^1$ which have nontrivial Dehn surgeries that yield $D^2\times S^1$, Topology Appl. 38 (1991) 1 MR1093862
8 F Bonahon, Difféotopies des espaces lenticulaires, Topology 22 (1983) 305 MR710104
9 F Bonahon, L C Siebenmann, The characteristic toric splitting of irreducible compact $3$–orbifolds, Math. Ann. 278 (1987) 441 MR909236
10 G E Bredon, J W Wood, Non-orientable surfaces in orientable $3$–manifolds, Invent. Math. 7 (1969) 83 MR0246312
11 M G Brin, Seifert fibered spaces: Notes for a course given in the spring of 1993 arXiv:0711.1346
12 D Buck, DNA topology, from: "Applications of knot theory" (editors D Buck, E Flapan), Proc. Symp. Appl. Math. 66, Amer. Math. Soc. (2009) 47 MR2508728
13 D Buck, K L Baker, Taxonomy of DNA conformations within complex nucleoprotein assemblies, from: "Statistical physics and topology of polymers with ramifications to structure and function of DNA and proteins" (editors T Deguchi, H Hayakawa, K Shimokawa, A Stasiak, K Tsurusaki), Progress Theor. Phys. Suppl. 191, Kyoto University (2011) 55
14 D Buck, E Flapan, Predicting knot or catenane type of site-specific recombination products, J. Mol. Biol. 374 (2007) 1186
15 D Buck, E Flapan, A topological characterization of knots and links arising from site-specific recombination, J. Phys. A 40 (2007) 12377 MR2394909
16 D Buck, M Mauricio, Connect sum of lens spaces surgeries: application to Hin recombination, Math. Proc. Cambridge Philos. Soc. 150 (2011) 505 MR2784772
17 D Buck, C Verjovsky Marcotte, Tangle solutions for a family of DNA-rearranging proteins, Math. Proc. Cambridge Philos. Soc. 139 (2005) 59 MR2155505
18 D Buck, C Verjovsky Marcotte, Classification of tangle solutions for integrases, a protein family that changes DNA topology, J. Knot Theory Ramifications 16 (2007) 969 MR2364885
19 G R Buck, E L Zechiedrich, DNA disentangling by type-$2$ topoisomerases, J. Mol. Biol. 340 (2004) 933
20 J H Conway, An enumeration of knots and links, and some of their algebraic properties, from: "Computational Problems in Abstract Algebra" (editor J Leech), Pergamon (1970) 329 MR0258014
21 M Culler, N M Dunfield, J R Weeks, SnapPy, a computer program for studying the geometry and topology of $3$–manifolds
22 M Culler, C M Gordon, J Luecke, P B Shalen, Dehn surgery on knots, Ann. of Math. 125 (1987) 237 MR881270
23 I K Darcy, J Luecke, M Vazquez, Tangle analysis of difference topology experiments: applications to a Mu protein-DNA complex, Algebr. Geom. Topol. 9 (2009) 2247 MR2558311
24 I K Darcy, D W Sumners, Rational tangle distances on knots and links, Math. Proc. Cambridge Philos. Soc. 128 (2000) 497 MR1744106
25 W D Dunbar, G R Meyerhoff, Volumes of hyperbolic $3$–orbifolds, Indiana Univ. Math. J. 43 (1994) 611 MR1291531
26 C Ernst, Tangle equations, J. Knot Theory Ramif. 5 (1996) 145 MR1395775
27 C Ernst, D W Sumners, A calculus for rational tangles: applications to DNA recombination, Math. Proc. Cambridge Philos. Soc. 108 (1990) 489 MR1068451
28 M Eudave-Muñoz, Primeness and sums of tangles, Trans. Amer. Math. Soc. 306 (1988) 773 MR933317
29 D Gabai, Foliations and the topology of $3$–manifolds, J. Differential Geom. 18 (1983) 445 MR723813
30 D Gabai, Surgery on knots in solid tori, Topology 28 (1989) 1 MR991095
31 D Gabai, $1$–bridge braids in solid tori, Topology Appl. 37 (1990) 221 MR1082933
32 C M Gordon, J Luecke, Knots are determined by their complements, J. Amer. Math. Soc. 2 (1989) 371 MR965210
33 C M Gordon, J Luecke, Knots with unknotting number 1 and essential Conway spheres, Algebr. Geom. Topol. 6 (2006) 2051 MR2263059
34 I Grainge, D Buck, M Jayaram, Geometry of site alignment during Int family recombination: antiparallel synapsis by the Flp recombinase, J. Mol. Biol. 298 (2000) 749
35 J E Greene, The lens space realization problem arXiv:1010.6257
36 N D Grindley, K L Whiteson, P A Rice, Mechanisms of site-specific recombination, Annu Rev Biochem 75 (2006) 567
37 M Hedden, On Floer homology and the Berge conjecture on knots admitting lens space surgeries, Trans. Amer. Math. Soc. 363 (2011) 949 MR2728591
38 W Heil, $3$–manifolds that are sums of solid tori and Seifert fiber spaces, Proc. Amer. Math. Soc. 37 (1973) 609 MR0356055
39 C Hodgson, J H Rubinstein, Involutions and isotopies of lens spaces, from: "Knot theory and manifolds" (editor D Rolfsen), Lecture Notes in Math. 1144, Springer (1985) 60 MR823282
40 N Hoffman, Commensurability classes containing three knot complements, Algebr. Geom. Topol. 10 (2010) 663 MR2606796
41 W Jaco, J H Rubinstein, PL equivariant surgery and invariant decompositions of $3$–manifolds, Adv. in Math. 73 (1989) 149 MR987273
42 W H Jaco, P B Shalen, Seifert fibered spaces in $3$–manifolds, Mem. Amer. Math. Soc. 21 (1979) MR539411
43 M Jankins, W D Neumann, Lectures on Seifert manifolds, Brandeis Lecture Notes 2, Brandeis University (1983) MR741334
44 K Johannson, Homotopy equivalences of $3$–manifolds with boundaries, Lecture Notes in Mathematics 761, Springer (1979) MR551744
45 P K Kim, J L Tollefson, Splitting the PL involutions of nonprime $3$–manifolds, Michigan Math. J. 27 (1980) 259 MR584691
46 R Kirby, Problems in low-dimensional topology, from: "Geometric topology" (editor R Kirby), AMS/IP Stud. Adv. Math. 2, Amer. Math. Soc. (1997) 35 MR1470751
47 P Kohn, Two-bridge links with unlinking number one, Proc. Amer. Math. Soc. 113 (1991) 1135 MR1079893
48 W B R Lickorish, Prime knots and tangles, Trans. Amer. Math. Soc. 267 (1981) 321 MR621991
49 P Lisca, Lens spaces, rational balls and the ribbon conjecture, Geom. Topol. 11 (2007) 429 MR2302495
50 Z Liu, R W Deibler, H S Chan, L Zechiedrich, The why and how of DNA unlinking, Nucleic Acids Res. 37 (2009) 661
51 Z Liu, J K Mann, E L Zechiedrich, H S Chan, Topological information embodied in local juxtaposition geometry provides a statistical mechanical basis for unknotting by type-2 DNA topoisomerases, J Mol. Biol. 361 (2006) 268
52 B Martelli, C Petronio, Dehn filling of the “magic” $3$–manifold, Comm. Anal. Geom. 14 (2006) 969 MR2287152
53 M Mecchia, Hyperbolic $2$–fold branched coverings, Rend. Istit. Mat. Univ. Trieste 32 (2001) 165 MR1893397
54 W H Meeks III, P Scott, Finite group actions on $3$–manifolds, Invent. Math. 86 (1986) 287 MR856847
55 J M Montesinos, Surgery on links and double branched covers of $S^{3}$, from: "Knots, groups, and $3$–manifolds (Papers dedicated to the memory of R. H. Fox)" (editor L P Neuwirth), Ann. of Math. Studies 84, Princeton Univ. Press (1975) 227 MR0380802
56 K Morimoto, M Sakuma, On unknotting tunnels for knots, Math. Ann. 289 (1991) 143 MR1087243
57 L Moser, Elementary surgery along a torus knot, Pacific J. Math. 38 (1971) 737 MR0383406
58 G D Mostow, Strong rigidity of locally symmetric spaces, Annals of Mathematics Studies 78, Princeton Univ. Press (1973) MR0385004
59 L Paoluzzi, On hyperbolic type involutions, Rend. Istit. Mat. Univ. Trieste 32 (2001) 221 MR1893400
60 G Prasad, Strong rigidity of $\mathbf{Q}$–rank $1$ lattices, Invent. Math. 21 (1973) 255 MR0385005
61 G L Randall, B M Pettitt, G R Buck, E L Zechiedriech, Electrostatics of DNA–DNA juxtapositions: consequences for type II topoisomerase function, J. Phys. Condens. Matter 18 (2006) 173
62 J Rasmussen, Lens space surgeries and $L$–space homology spheres arXiv:0710.2531
63 D Rolfsen, Knots and links, Mathematics Lecture Series 7, Publish or Perish (1990) MR1277811
64 Y W Rong, Some knots not determined by their complements, from: "Quantum topology" (editors L H Kauffman, R A Baadhio), Ser. Knots Everything 3, World Sci. Publ., River Edge, NJ (1993) 339 MR1273583
65 M Scharlemann, Sutured manifolds and generalized Thurston norms, J. Differential Geom. 29 (1989) 557 MR992331
66 S A Taylor, Boring split links, Pacific J. Math. 241 (2009) 127 MR2485461
67 W P Thurston, Three-dimensional geometry and topology. Vol. 1, Princeton Mathematical Series 35, Princeton Univ. Press (1997) MR1435975
68 J L Tollefson, A $3$–manifold admitting a unique periodic PL map, Michigan Math. J. 21 (1974) 7 MR0350740
69 J L Tollefson, Involutions of Seifert fiber spaces, Pacific J. Math. 74 (1978) 519 MR0645400
70 I Torisu, The determination of the pairs of two-bridge knots or links with Gordian distance one, Proc. Amer. Math. Soc. 126 (1998) 1565 MR1425140
71 S Trigueros, J Salceda, I Bermudez, X Fernandez, J Roca, Asymmetric removal of supercoils suggests how topoisomerase II simplifies DNA topology, J. Mol. Biol. 335 (2004) 723
72 M Vazquez, D W Sumners, Tangle analysis of Gin site-specific recombination, Math. Proc. Cambridge Philos. Soc. 136 (2004) 565 MR2055047
73 A Vologodskii, Theoretical models of DNA topology simplification by type IIA DNA topoisomerases, Nucleic Acids Res. 37 (2009) 3125
74 A V Vologodskii, W Zhang, V Rybenkov, A A Podtelezhnikov, D Subramanian, J D Griffith, N R Cozzarelli, Mechanism of topology simplification by type II DNA topoisomerase, Proc. Nat. Acad. Sci. 98 (2001) 3045
75 F Waldhausen, On irreducible $3$–manifolds which are sufficiently large, Ann. of Math. 87 (1968) 56 MR0224099
76 S C Wang, Q Zhou, Symmetry of knots and cyclic surgery, Trans. Amer. Math. Soc. 330 (1992) 665 MR1031244
77 Y Q Wu, The classification of nonsimple algebraic tangles, Math. Ann. 304 (1996) 457 MR1375620
78 J Yan, M O Magnasco, J F Marko, A kinetic proofreading mechanism for disentanglement of DNA by topoisomerases, Nature 401 (1999) 932