Algebraic & Geometric Topology Volume 22, issue 5 (2022)

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ISSN (electronic): 1472-2739

ISSN (print): 1472-2747

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Cusp volumes of alternating knots on surfaces

Brandon Bavier

Algebraic & Geometric Topology 22 (2022) 2467–2532

DOI: 10.2140/agt.2022.22.2467

Bibliography

1	C C Adams, Toroidally alternating knots and links, Topology 33 (1994) 353 MR1273788
2	C Adams, Bipyramids and bounds on volumes of hyperbolic links, Topology Appl. 222 (2017) 100 MR3630197
3	C Adams, Waist size for cusps in hyperbolic 3–manifolds, II, Geom. Dedicata 203 (2019) 53 MR4027583
4	C Adams, C Albors-Riera, B Haddock, Z Li, D Nishida, B Reinoso, L Wang, Hyperbolicity of links in thickened surfaces, Topology Appl. 256 (2019) 262 MR3916014
5	C Adams, A Colestock, J Fowler, W Gillam, E Katerman, Cusp size bounds from singular surfaces in hyperbolic 3–manifolds, Trans. Amer. Math. Soc. 358 (2006) 727 MR2177038
6	C Adams, T Fleming, M Levin, A M Turner, Crossing number of alternating knots in S × I, Pacific J. Math. 203 (2002) 1 MR1895923
7	I Agol, Bounds on exceptional Dehn filling, Geom. Topol. 4 (2000) 431 MR1799796
8	B Bavier, Diagrammatic and geometric invariants of hyperbolic weakly generalized alternating knots, PhD thesis, Michigan State University (2021) MR4297584
9	S D Burton, E Kalfagianni, Geometric estimates from spanning surfaces, Bull. Lond. Math. Soc. 49 (2017) 694 MR3725490
10	A Champanerkar, I Kofman, J S Purcell, Geometry of biperiodic alternating links, J. Lond. Math. Soc. 99 (2019) 807 MR3977891
11	D Cooper, M Lackenby, Dehn surgery and negatively curved 3–manifolds, J. Differential Geom. 50 (1998) 591 MR1690741
12	M Culler, N M Dunfield, M Goerner, J R Weeks, SnapPy, a computer program for studying the geometry and topology of 3–manifolds
13	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
14	D B A Epstein, R C Penner, Euclidean decompositions of noncompact hyperbolic manifolds, J. Differential Geom. 27 (1988) 67 MR918457
15	D Futer, E Kalfagianni, J S Purcell, Dehn filling, volume, and the Jones polynomial, J. Differential Geom. 78 (2008) 429 MR2396249
16	D Futer, E Kalfagianni, J S Purcell, Symmetric links and Conway sums : volume and Jones polynomial, Math. Res. Lett. 16 (2009) 233 MR2496741
17	D Futer, E Kalfagianni, J S Purcell, Cusp areas of Farey manifolds and applications to knot theory, Int. Math. Res. Not. 2010 (2010) 4434 MR2739802
18	D Futer, E Kalfagianni, J Purcell, Guts of surfaces and the colored Jones polynomial, 2069, Springer (2013) MR3024600
19	D Futer, E Kalfagianni, J S Purcell, Hyperbolic semi-adequate links, Comm. Anal. Geom. 23 (2015) 993 MR3458811
20	D Futer, E Kalfagianni, J S Purcell, A survey of hyperbolic knot theory, from: "Knots, low-dimensional topology and applications" (editors C C Adams, C M Gordon, V F R Jones, L H Kauffman, S Lambropoulou, K C Millett, J H Przytycki, R Ricca, R Sazdanovic), Springer Proc. Math. Stat. 284, Springer (2019) 1 MR3986038
21	D Futer, J S Purcell, Links with no exceptional surgeries, Comment. Math. Helv. 82 (2007) 629 MR2314056
22	C Hayashi, Links with alternating diagrams on closed surfaces of positive genus, Math. Proc. Cambridge Philos. Soc. 117 (1995) 113 MR1297898
23	J A Howie, J S Purcell, Geometry of alternating links on surfaces, Trans. Amer. Math. Soc. 373 (2020) 2349 MR4069222
24	J A Howie, J H Rubinstein, Weakly generalised alternating links, in preparation
25	E Kalfagianni, J S Purcell, Alternating links on surfaces and volume bounds, preprint (2020) arXiv:2004.10909
26	R C Kirby editor, Problems in low-dimensional topology, from: "Geometric topology", AMS/IP Stud. Adv. Math. 2, Amer. Math. Soc. (1997) 35 MR1470751
27	M Lackenby, Word hyperbolic Dehn surgery, Invent. Math. 140 (2000) 243 MR1756996
28	M Lackenby, The volume of hyperbolic alternating link complements, Proc. Lond. Math. Soc. 88 (2004) 204 MR2018964
29	M Lackenby, J S Purcell, Cusp volumes of alternating knots, Geom. Topol. 20 (2016) 2053 MR3548463
30	M Lackenby, J S Purcell, Essential twisted surfaces in alternating link complements, Algebr. Geom. Topol. 16 (2016) 3209 MR3584257
31	W Menasco, Closed incompressible surfaces in alternating knot and link complements, Topology 23 (1984) 37 MR721450
32	J K Osoinach Jr., Manifolds obtained by surgery on an infinite number of knots in S³, Topology 45 (2006) 725 MR2236375
33	M Ozawa, Non-triviality of generalized alternating knots, J. Knot Theory Ramifications 15 (2006) 351 MR2217501
34	G Prasad, Strong rigidity of ℚ–rank 1 lattices, Invent. Math. 21 (1973) 255 MR385005
35	J S Purcell, Cusp shapes under cone deformation, J. Differential Geom. 80 (2008) 453 MR2472480
36	W Thurston, Geometry and topology of three-manifolds, lecture notes (1980)