Charles Livingston

Charles Livingston

Professor Emeritus of Mathematics
Indiana University, Bloomington

Resources

Publications

Preprints
2. The computation of higher order Alexander invariants. arXiv
1. Knot primality: knot Floer homology, metacyclic representations and twisted homology, joint with Samantha Allen. arXiv
Published and Accepted Articles
102. Using knot Floer invariants to detect prime knots, joint with Samantha Allen, Misha Temkin, and C.-M. Michael Wong. arXiv. To appear, Pac. J. Math.
101. Signed clasp numbers and four-genus bounds, New York J. Math. 31 (2025) 1316-1323. arXiv.
100. An Upsilon torsion function for knot Floer homology, joint with Samantha Allen, Math. Res. Lett. 32 (2025), no. 3, 679-705. arXiv
99. Rank-expanding satellite operators on the topological knot concordance group. arXiv. To appear, Michigan Journal of Mathematics.
98. Cobordism distance on the projective space of the knot concordance group, Canadian Journal of Mathematics 76 (2024) 1267–1288. Reprint arXiv
97. Connected sums of codimension two locally flat submanifolds, Proc. Roy. Soc. Edinburgh Sect. A 154 (2024), 1937–1944. arXiv
96. Branched covers and rational homology balls, Algebraic and Geometric Topology 24-1 (2024), 587–594. arXiv
95. Critical point counts in knot cobordisms: abelian and metacyclic invariants, Trans. AMS (2023), 171–200. arXiv
94. Intrinsic symmetry groups of links, Algebraic and Geometric Topology 23 (2023) 2347–2368. arXiv
93. Knot reversal and mutation act non-trivially on the concordance group of topologically slice knots, Selecta Mathematica 28, Article 38 (2022). Joint with Taehee Kim. arXiv
92. The cobordism distance between a knot and its reverse, Proc. Amer. Math. Soc. 150 (2022), 1811–1819. arXiv
91. Null-homologous unknottings, IRMA Lectures in Mathematics and Theoretical Physics Vol. 33 (2021), 59–68. arXiv
90. Primary decompositions of knot concordance, New York J. of Math. 27 (2021), 776–786. arXiv
89. Chiral smoothings of knots, Proc. Edin. Math. Soc. 63 (2020), 1048–1061. arXiv
88. Unknotting with a single twist, L’Enseignement Mathématique 66 (2020) 541–589. Joint with Samantha Allen. arXiv
87. Signature invariants related to the unknotting number, Pac. J. Math. 305 (2020), 229–250. arXiv
86. Signature functions of knots, Proc. Amer. Math. Soc. 146 (2018), 4513–4520. arXiv
85. Secondary Upsilon invariants of knots, Quarterly Journal of Mathematics 69 (2018) 799–813. Joint with Se-Goo Kim. arXiv
84. The four-genus of connected sums of torus knots, Math. Proc. Cambridge Phil. Soc. 164 (2018) 531–550. Joint with Cornelia Van Cott. arXiv
83. Concordances from connected sums of torus knots to L-space knots, New York J. of Math. 24 (2018) 233–239. Reprint arXiv
82. Splitting numbers of links and the four-genus, Proc. Amer. Math. Soc. 146 (2018) 421–427. Reprint arXiv
81. Plane algebraic curves of arbitrary genus via Heegaard Floer homology, Comment. Math. Helvetici 92 (2017) 215–256. Joint with Maciej Borodzik and Matt Hedden. arXiv
80. Knot concordance and alternating knots, Mich. Math. J. 66 (2017) 421–432. Joint with Stefan Friedl and Raphael Zentner. arXiv
79. Notes on the knot concordance invariant Upsilon, Algebraic and Geometric Topology 17 (2017) 111–130. arXiv AGT
78. Signature Jumps and Alexander Polynomials for Links, Proc. AMS 144 (2016) 5407–5417. Joint with Pat Gilmer. arXiv Reprint
77. Semigroups, d-invariants and deformations of cuspidal singular points of plane curves, joint with Maciej Borodzik. J. London Math. Soc. 93 (2016), 439–463. arXiv
76. Topologically slice knots of smooth concordance order two, joint with Matt Hedden and Se-Goo Kim. J. Differential Geometry 102 (2016), 353–393. Reprint arXiv
75. Doubly slice knots with low crossing number, joint with Jeff Meier. New York Journal of Mathematics 21 (2015), 1008–1026. Reprint arXiv
74. The concordance classification of low crossing number knots, joint with Julia Collins and Paul Kirk. Proc. AMS (2015), 4525–4536. Published arXiv Reprint
73. Heegaard Floer homology and rational cuspidal curves, Forum of Mathematics, Sigma 2 (2014), 23 pages. Joint with Maciej Borodzik. arXiv
72. Non-splittability of the rational homology cobordism group, Pac. J. Math. 271 (2014) 183–211. Joint with Se-Goo Kim. arXiv
71. On surgery curves for genus one slice knots, Pac. J. Math. 265 (2013), 405–425. Joint with Patrick M. Gilmer. arXiv
70. Non-slice linear combinations of algebraic knots, J. European Math. Society 14 (2012), issue 4, 1181–1208. Joint with Matthew Hedden and Paul Kirk. arXiv
69. Topologically slice knots with nontrivial Alexander polynomial, Adv. in Math. 231 (2012), 913–939. Joint with Matt Hedden and Danny Ruberman. arXiv
68. The nonorientable four-genus of knots, J. Lond. Math. Soc. (2) 84 (2011), no. 3, 559–577. Joint with Pat Gilmer. arXiv
67. The algebraic concordance order of a knot, J. Knot Theory and its Ramifications 12 (2011), 1693–1711. arXiv
66. Knot 4-genus and the rank of a class in W(Q(t)), Pac. J. of Math. (2011), 113–126. arXiv
65. Concordance of Bing Doubles and Boundary Genus, Math. Proc. Camb. Phil. Soc. 151 (2011), 459–470. Joint with C. Van Cott. arXiv Reprint
64. The stable 4-genus of knots, Algebraic & Geometric Topology 10 (2010) 2191–2202. arXiv Reprint
63. Stabilizing Four-Torsion in Classical Knot Concordance, Topology Proceedings 37 (2010), 119–128. Joint with Swatee Naik. arXiv
62. Metabelian representations, twisted Alexander polynomials, knot slicing, and mutation, Mathematische Zeitschrift 265 (2010) 925–949. Joint with C. Herald and P. Kirk. arXiv Reprint
61. The geography problem for 4-manifolds with specified fundamental group, Trans. Amer. Math. Soc. 361 (2009) 4091–4124. Joint with P. Kirk. arXiv Reprint
60. The concordance genus of a knot, II, Algebraic & Geometric Topology 9 (2009) 167–185. arXiv Reprint
59. Algebraic and Heegaard-Floer invariants of knots with slice Bing doubles, Math. Proc. Cambridge Phil. Soc. 144 (2008) 403–410. Joint with J. C. Cha and D. Ruberman. arXiv Reprint
58. Concordance Crosscap Numbers of Knots and the Alexander Polynomial, Proc. Amer. Math. Soc. 136 (2008) 3351–3353. arXiv Reprint
57. Slice knots with distinct Ozsvath-Szabo and Rasmussen invariants, Proc. Amer. Math. Soc. 136 (2008) 347–349. arXiv Reprint
56. Ozsvath-Szabo and Rasmussen invariants of doubled knots, Alg. and Geom. Top. 6 (2006) 651–657. Joint with S. Naik. arXiv Reprint
55. Twisted Alexander polynomials of periodic knots, Alg. and Geo. Topology 6 (2006) 145–169. Joint with J. Hillman and S. Naik. arXiv Reprint
54. Knot mutation: 4-genus of knots and algebraic concordance, Pac. J. of Math. 220 (2005) 87–106. Joint with S. Kim. arXiv Reprint
53. A survey of classical knot concordance, The Handbook of Knot Theory (2005). arXiv
52. The Hausmann-Weinberger 4-manifold invariant of abelian groups, Proc. Amer. Math. Soc. 133 (2005) 1537–1546. Joint with P. Kirk. arXiv Reprint
51. Four-manifolds of large negative deficiency, Math. Proc. Camb. 138 (2005) 107–115. arXiv Reprint
50. Computations of the Ozsvath-Szabo knot concordance invariant, Geo. and Top. 8 (2004) 735–742. arXiv
49. Knot signatures are independent, Proc. Amer. Math. Soc. 132 (2004) 2809–2816. Joint with J. C. Cha. arXiv Reprint
48. The concordance genus of knots, Alg. and Geom. Top. 4 (2004) 1–22. arXiv Reprint
47. Splitting the concordance group of algebraically slice knots, Geometry and Topology 7 (2003) 641–643. arXiv Reprint
46. Enhanced linking numbers, American Mathematical Monthly 110 (2003) 361–385. Reprint
45. Observations on Lickorish knotting of contractible 4-manifolds, Pac. J. of Math. 209 (2003) 319–324. arXiv Reprint
44. The slicing number of a knot, Algebraic and Geometric Topology 2 (2002) 1051–1060. arXiv Reprint
43. New examples of non-slice, algebraically slice knots, Proc. Amer. Math. Soc. 130 (2002) 1551–1555. arXiv Reprint
42. Concordance and mutation, Geometry and Topology 5 (2001) 831–883. Joint with P. Kirk. arXiv
41. Seifert forms and concordance, Geometry and Topology 6 (2002) 403–408. arXiv Reprint
40. Knot concordance and torsion, Asian Journal of Mathematics 5 (2001) 161–168. Joint with S. Naik. arXiv Reprint
39. The Gassner representation for string links, Comm. Cont. Math. 3 (2001) 87–136. Joint with P. Kirk and Z. Wang. arXiv
38. Infinite order amphicheiral knots, Algebraic and Geometric Topology 1 (2001) 231–241. arXiv Reprint
37. Knot invariants in 3-manifolds, essential tori, and the first cohomology of the free loop space on M, Pacific Journal of Mathematics 197 (2001) 73–96. Joint with P. Kirk. Reprint
36. Maps of surface groups to finite groups with no simple loops in the kernel, Journal of Knot Theory and its Ramifications 9 (2000) 1029–1036. arXiv Reprint
35. Order 2 Algebraically slice knots, Geometry and Topology Monographs II: Proceedings of the Kirbyfest (1999), 335–342. arXiv Reprint
34. Obstructing four-torsion in the classical knot concordance group, J. Diff. Geom. 51 (1999) 1–12. Joint with S. Naik. arXiv Reprint
33. Twisted knot polynomials: inversion, mutation and concordance, Topology 38 (1999) 663–671. Joint with P. Kirk. Reprint
32. Twisted Alexander invariants, Reidemeister torsion, and Casson-Gordon invariants, Topology 38 (1999) 635–661. Joint with P. Kirk. Reprint
31. Type 1 invariants in irreducible 3-manifolds, Pac. J. of Math. 183 (1998) 305–331. Joint with P. Kirk. Reprint
30. Vassiliev Invariants of two component links and the Casson-Walker invariant, Topology 36 (1997) 1333–1353. Joint with P. Kirk. Reprint
29. Embedding punctured lens spaces in four-manifolds, Comment. Math. Helvetici 71 (1996) 169–191. Joint with A. Edmonds. Reprint
28. Knotted symmetric graphs, Proc. Amer. Math. Soc. 123 (1995) 963–967. Reprint
27. Lifting knot group representations, Journal of Knot Theory and its Ramifications 4 (1995) 225–234. Reprint
26. The Casson-Gordon invariant and link concordance, Topology 31 (1992) 475–492. Joint with P. Gilmer. Reprint
25. Discriminants of Casson-Gordon invariants, Math. Proc. Camb. Phil. Soc. 112 (1992) 127–139. Joint with P. Gilmer. Reprint
24. Exotic dihedral actions on homology 3-spheres, Topology and its Applications 39 (1991) 153–158. Reprint
23. Periodic knots and Maple, Notices of A.M.S. 38 (1991) 785–788. (Expository article.)
22. Alexander polynomials of periodic knots, Topology 30 (1991) 551–564. Joint with J. Davis. Reprint
21. An algebraic concordance group for (p, 2p−1)-links in S(2p+1), Proc. Edinburgh Math. Soc. 34 (1991) 455–462. Joint with P. Gilmer. Reprint
20. Periodic knots, Smith theory and Murasugi’s congruence, L’Enseignement Mathématique 37 (1991) 1–9. Joint with J. Davis. Reprint
19. Links not concordant to boundary links, Proc. Amer. Math. Soc. 110 (1991) 1129–1131. Reprint
18. Peripherally specified homomorphs of knot groups, Transactions of the AMS 311 (1989) 135–146. Joint with D. Johnson. Reprint
17. The free genus of doubled knots, Proc. Amer. Math. Soc. 104 (1988) 329–333. Reprint
16. Indecomposable surfaces in 4-space, Pacific J. of Math. 132 (1988) 371–378. Reprint
15. Knots with finite weight commutator subgroups, Proc. Amer. Math. Soc. 101 (1987) 195–198. Reprint
14. Companionship and knot group representations, Topology and Its Applications 25 (1987) 241–244. Reprint
13. Abelian invariants of satellite knots, Springer Lecture Notes in Mathematics 1167 (1986) 217–228. Joint with P. Melvin. Reprint
12. Inequivalent, bordant group actions on a surface, Math. Proc. Camb. Phil. Soc. 99 (1986) 233–238. Reprint
11. Mazur manifolds and wrapping number of knots in S1×S2, Houston J. of Math. (1985) 523–533. Reprint
10. Stabilizing surface symmetries, Michigan Math. J. 32 (1985) 249–255. Reprint
9. Stably irreducible surfaces in S4, Pacific J. of Math. 116 (1985) 77–84. Reprint
8. Symmetric representations of knot groups, Topology and Its Applications 18 (1984) 281–312. Joint with A. Edmonds. Reprint
7. Group actions on fibered 3-manifolds, Comm. Math. Helv. 58 (1983) 529–542. Joint with A. Edmonds. Reprint
6. Algebraic knots are algebraically dependent, Proc. Amer. Math. Soc. 87 (1983) 179–180. Joint with P. Melvin. Reprint
5. Knots which are not concordant to their reverses, Oxford Q. J. of Math. 34 (1983) 323–328. Reprint
4. Embedding 3-manifolds in S4, Topology 22 (1983) 241–252. Joint with P. Gilmer. Reprint
3. More 3-manifolds with multiple knot surgery and branched-cover descriptions, Math. Proc. Camb. Phil. Soc. 91 (1982) 473–475. Reprint
2. Surfaces bounding the unlink, Michigan Math. J. 29 (1982) 289–298. Reprint
1. Homology cobordisms of 3-manifolds, knot concordances, and prime knots, Pacific J. of Math. 94 (1981) 193–206. Reprint