Volume 5, issue 2 (2001)

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Concordance and mutation

Paul A Kirk and Charles Livingston

Geometry & Topology 5 (2001) 831–883
Bibliography
1 S Akbulut, R Kirby, Branched covers of surfaces in 4–manifolds, Math. Ann. 252 (1979/80) 111 MR593626
2 M F Atiyah, V K Patodi, I M Singer, Spectral asymmetry and Riemannian geometry II, Math. Proc. Cambridge Philos. Soc. 78 (1975) 405 MR0397798
3 G E Bredon, Introduction to compact transformation groups, Pure and Applied Mathematics 46, Academic Press (1972) MR0413144
4 G Burde, H Zieschang, Knots, de Gruyter Studies in Mathematics 5, Walter de Gruyter & Co. (1985) MR808776
5 A J Casson, C M Gordon, Cobordism of classical knots, from: "À la recherche de la topologie perdue", Progr. Math. 62, Birkhäuser (1986) 181 MR900252
6 A J Casson, C M Gordon, On slice knots in dimension three, from: "Algebraic and geometric topology (Proc. Sympos. Pure Math., Stanford Univ., Stanford, Calif., 1976), Part 2", Proc. Sympos. Pure Math., XXXII, Amer. Math. Soc. (1978) 39 MR520521
7 J C Cha, K H Ko, On equivariant slice knots, Proc. Amer. Math. Soc. 127 (1999) 2175 MR1605928
8 T D Cochran, R E Gompf, Applications of Donaldson's theorems to classical knot concordance, homology 3–spheres and property $P$, Topology 27 (1988) 495 MR976591
9 T D Cochran, K E Orr, P Teichner, Knot concordance, Whitney towers and $L^2$–signatures, Ann. of Math. $(2)$ 157 (2003) 433 MR1973052
10 P E Conner, E E Floyd, Differentiable periodic maps, Ergebnisse der Mathematik und ihrer Grenzgebiete 33, Academic Press (1964) MR0176478
11 D Coray, F Michel, Knot cobordism and amphicheirality, Comment. Math. Helv. 58 (1983) 601 MR728455
12 S K Donaldson, An application of gauge theory to four-dimensional topology, J. Differential Geom. 18 (1983) 279 MR710056
13 R H Fox, A quick trip through knot theory, from: "Topology of 3–manifolds and related topics (Proc. The Univ. of Georgia Institute, 1961)", Prentice-Hall (1962) 120 MR0140099
14 R H Fox, J W Milnor, Singularities of 2–spheres in 4–space and cobordism of knots, Osaka J. Math. 3 (1966) 257 MR0211392
15 M H Freedman, The topology of four-dimensional manifolds, J. Differential Geom. 17 (1982) 357 MR679066
16 M H Freedman, F Quinn, Topology of 4–manifolds, Princeton Mathematical Series 39, Princeton University Press (1990) MR1201584
17 P M Gilmer, Slice knots in $S^{3}$, Quart. J. Math. Oxford Ser. $(2)$ 34 (1983) 305 MR711523
18 P Gilmer, C Livingston, The Casson–Gordon invariant and link concordance, Topology 31 (1992) 475 MR1174253
19 P Gilmer, C Livingston, Discriminants of Casson–Gordon invariants, Math. Proc. Cambridge Philos. Soc. 112 (1992) 127 MR1162937
20 , Knot theory, Lecture Notes in Mathematics 685, Springer (1978) MR0645392
21 C M Herald, Flat connections, the Alexander invariant, and Casson's invariant, Comm. Anal. Geom. 5 (1997) 93 MR1456309
22 C M Herald, Existence of irreducible representations for knot complements with nonconstant equivariant signature, Math. Ann. 309 (1997) 21 MR1467643
23 M Heusener, J Kroll, Deforming abelian $\mathrm{SU}(2)$–representations of knot groups, Comment. Math. Helv. 73 (1998) 480 MR1633375
24 B J Jiang, A simple proof that the concordance group of algebraically slice knots is infinitely generated, Proc. Amer. Math. Soc. 83 (1981) 189 MR620010
25 A Kawauchi, Topological imitation, mutation and the quantum $\mathrm{SU}(2)$ invariants, J. Knot Theory Ramifications 3 (1994) 25 MR1265451
26 C Kearton, Mutation of knots, Proc. Amer. Math. Soc. 105 (1989) 206 MR929430
27 M A Kervaire, Knot cobordism in codimension two, from: "Manifolds–Amsterdam 1970 (Proc. Nuffic Summer School)", Lecture Notes in Mathematics 197, Springer (1971) 83 MR0283786
28 R Kirby, Problems in low dimensional manifold theory, from: "Algebraic and geometric topology (Proc. Sympos. Pure Math., Stanford Univ., Stanford, Calif., 1976), Part 2", Proc. Sympos. Pure Math., XXXII, Amer. Math. Soc. (1978) 273 MR520548
29 R Kirby, Problems in low-dimensional topology, from: "Geometric topology (Athens, GA, 1993)", AMS/IP Stud. Adv. Math. 2, Amer. Math. Soc. (1997) 35 MR1470751
30 R C Kirby, W B R Lickorish, Prime knots and concordance, Math. Proc. Cambridge Philos. Soc. 86 (1979) 437 MR542689
31 P Kirk, C Livingston, Twisted knot polynomials: inversion, mutation and concordance, Topology 38 (1999) 663 MR1670424
32 P Kirk, C Livingston, Twisted Alexander invariants, Reidemeister torsion, and Casson–Gordon invariants, Topology 38 (1999) 635 MR1670420
33 J Levine, Knot cobordism groups in codimension two, Comment. Math. Helv. 44 (1969) 229 MR0246314
34 J Levine, Invariants of knot cobordism, Invent. Math. 8 (1969) 98 MR0253348
35 W B R Lickorish, Distinct 3–manifolds with all $\mathrm{SU}(2)_q$ invariants the same, Proc. Amer. Math. Soc. 117 (1993) 285 MR1129882
36 R Litherland, A formula for the Casson–Gordon invariant of a knot, preprint (1980)
37 R A Litherland, Cobordism of satellite knots, from: "Four-manifold theory (Durham, N.H., 1982)", Contemp. Math. 35, Amer. Math. Soc. (1984) 327 MR780587
38 C Livingston, Homology cobordisms of 3–manifolds, knot concordances, and prime knots, Pacific J. Math. 94 (1981) 193 MR625818
39 C Livingston, Knots which are not concordant to their reverses, Quart. J. Math. Oxford Ser. $(2)$ 34 (1983) 323 MR711524
40 C Livingston, Order 2 algebraically slice knots, from: "Proceedings of the Kirbyfest (Berkeley, CA, 1998)", Geom. Topol. Monogr. 2, Geom. Topol. Publ., Coventry (1999) 335 MR1734416
41 C Livingston, S Naik, Obstructing four-torsion in the classical knot concordance group, J. Differential Geom. 51 (1999) 1 MR1703602
42 R Meyerhoff, D Ruberman, Mutation and the $\eta$–invariant, J. Differential Geom. 31 (1990) 101 MR1030667
43 R Myers, Homology cobordisms, link concordances, and hyperbolic 3–manifolds, Trans. Amer. Math. Soc. 278 (1983) 271 MR697074
44 H R Morton, P Traczyk, The Jones polynomial of satellite links around mutants, from: "Braids (Santa Cruz, CA, 1986)", Contemp. Math. 78, Amer. Math. Soc. (1988) 587 MR975096
45 D Mullins, The generalized Casson invariant for 2–fold branched covers of $S^3$ and the Jones polynomial, Topology 32 (1993) 419 MR1217078
46 K Murasugi, On a certain numerical invariant of link types, Trans. Amer. Math. Soc. 117 (1965) 387 MR0171275
47 K Murasugi, Knot theory and its applications, Birkhäuser (1996) MR1391727
48 S Naik, Casson–Gordon invariants of genus one knots and concordance to reverses, J. Knot Theory Ramifications 5 (1996) 661 MR1414093
49 S Naik, Equivariant concordance of knots in $S^3$, from: "KNOTS '96 (Tokyo)", World Sci. Publ., River Edge, NJ (1997) 81 MR1664952
50 J Porti, Torsion de Reidemeister pour les variétés hyperboliques, Mem. Amer. Math. Soc. 128 (1997) MR1396960
51 D Rolfsen, Knots and links, Mathematics Lecture Series 7, Publish or Perish (1976) MR0515288
52 Y W Rong, Mutation and Witten invariants, Topology 33 (1994) 499 MR1286928
53 D Ruberman, Mutation and volumes of knots in $S^3$, Invent. Math. 90 (1987) 189 MR906585
54 L Rudolph, An obstruction to sliceness via contact geometry and “classical” gauge theory, Invent. Math. 119 (1995) 155 MR1309974
55 J P Serre, Linear representations of finite groups, Graduate Texts in Mathematics 42, Springer (1977) MR0450380
56 A G Tristram, Some cobordism invariants for links, Proc. Cambridge Philos. Soc. 66 (1969) 251 MR0248854
57 H F Trotter, On $S$–equivalence of Seifert matrices, Invent. Math. 20 (1973) 173 MR0645546
58 H F Trotter, Non-invertible knots exist, Topology 2 (1963) 275 MR0158395
59 K Walker, An extension of Casson's invariant, Annals of Mathematics Studies 126, Princeton University Press (1992) MR1154798
60 C T C Wall, Non-additivity of the signature, Invent. Math. 7 (1969) 269 MR0246311
61 E Witten, Monopoles and four-manifolds, Math. Res. Lett. 1 (1994) 769 MR1306021