Algebraic & Geometric Topology Volume 4, issue 2 (2004)

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Eta invariants as sliceness obstructions and their relation to Casson–Gordon invariants

Stefan Friedl

Algebraic & Geometric Topology 4 (2004) 893–934

DOI: 10.2140/agt.2004.4.893

Bibliography

1	M F Atiyah, Elliptic operators, discrete groups and von Neumann algebras, from: "Colloque “Analyse et Topologie” en l'Honneur de Henri Cartan (Orsay, 1974)", Soc. Math. France (1976) MR0420729
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	R C Blanchfield, Intersection theory of manifolds with operators with applications to knot theory, Ann. of Math. $(2)$ 65 (1957) 340 MR0085512
4	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
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	J Cheeger, M Gromov, Bounds on the von Neumann dimension of $L^2$–cohomology and the Gauss–Bonnet theorem for open manifolds, J. Differential Geom. 21 (1985) 1 MR806699
7	T D Cochran, K E Orr, P Teichner, Knot concordance, Whitney towers and $L^2$–signatures, Ann. of Math. $(2)$ 157 (2003) 433 MR1973052
8	T D Cochran, K E Orr, P Teichner, Structure in the classical knot concordance group, Comment. Math. Helv. 79 (2004) 105 MR2031301
9	P E Conner, E E Floyd, Differentiable periodic maps, Ergebnisse der Mathematik und ihrer Grenzgebiete, N. F., Band 33, Academic Press (1964) MR0176478
10	R H Fox, Some problems in knot theory, from: "Topology of 3–manifolds and related topics (Proc. The Univ. of Georgia Institute, 1961)", Prentice-Hall (1962) 168 MR0140100
11	M H Freedman, F Quinn, Topology of 4–manifolds, Princeton Mathematical Series 39, Princeton University Press (1990) MR1201584
12	S Friedl, Full signature invariants for $L_0(F(t))$, Proc. Amer. Math. Soc. 133 (2005) 647 MR2113910
13	S Friedl, Link concordance, boundary link concordance and eta-invariants, Math. Proc. Cambridge Philos. Soc. 138 (2005) 437 MR2138572
14	S Friedl, $L^2$–eta-invariants and their approximation by unitary eta-invariants, Math. Proc. Cambridge Philos. Soc. 138 (2005) 327 MR2132174
15	S Friedl, Eta invariants as sliceness obstructions and their relation to Casson–Gordon invariants, Algebr. Geom. Topol. 4 (2004) 893 MR2100685
16	P M Gilmer, Slice knots in $S^{3}$, Quart. J. Math. Oxford Ser. $(2)$ 34 (1983) 305 MR711523
17	P Gilmer, Classical knot and link concordance, Comment. Math. Helv. 68 (1993) 1 MR1201199
18	R E Gompf, Smooth concordance of topologically slice knots, Topology 25 (1986) 353 MR842430
19	C M Gordon, Some aspects of classical knot theory, from: "Knot theory (Proc. Sem., Plans-sur–Bex, 1977)", Lecture Notes in Math. 685, Springer (1978) 1 MR521730
20	C M Gordon, Ribbon concordance of knots in the 3–sphere, Math. Ann. 257 (1981) 157 MR634459
21	P J Hilton, U Stammbach, A course in homological algebra, Graduate Texts in Mathematics 4, Springer (1971) MR0346025
22	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
23	C Kearton, Classification of simple knots by Blanchfield duality, Bull. Amer. Math. Soc. 79 (1973) 952 MR0324706
24	C Kearton, Presentations of $n$–knots, Trans. Amer. Math. Soc. 202 (1975) 123 MR0358795
25	C Kearton, Cobordism of knots and Blanchfield duality, J. London Math. Soc. $(2)$ 10 (1975) 406 MR0385873
26	M A Kervaire, On higher dimensional knots, from: "Differential and Combinatorial Topology (A Symposium in Honor of Marston Morse)", Princeton Univ. Press (1965) 105 MR0178475
27	T Kim, Filtration of the classical knot concordance group and Casson–Gordon invariants, Math. Proc. Cambridge Philos. Soc. 137 (2004) 293 MR2092061
28	T Kim, Obstructions to slicing and doubly slicing knots, PhD thesis, Indiana University, Bloomington (2003)
29	T Kim, New obstructions to doubly slicing knots, Topology 45 (2006) 543 MR2218756
30	S Lang, Algebra, Graduate Texts in Mathematics 211, Springer (2002) MR1878556
31	C Letsche, An obstruction to slicing knots using the eta invariant, PhD thesis, Indiana University, Bloomington (1995)
32	C F Letsche, An obstruction to slicing knots using the eta invariant, Math. Proc. Cambridge Philos. Soc. 128 (2000) 301 MR1735303
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 $(1969)$, 98–110; addendum, ibid. 8 (1969) 355 MR0253348
35	J Levine, An algebraic classification of some knots of codimension two, Comment. Math. Helv. 45 (1970) 185 MR0266226
36	J Levine, Knot modules I, Trans. Amer. Math. Soc. 229 (1977) 1 MR0461518
37	J P Levine, Metabolic and hyperbolic forms from knot theory, J. Pure Appl. Algebra 58 (1989) 251 MR1004605
38	J P Levine, Link invariants via the eta invariant, Comment. Math. Helv. 69 (1994) 82 MR1259607
39	R A Litherland, Cobordism of satellite knots, from: "Four-manifold theory (Durham, N.H., 1982)", Contemp. Math. 35, Amer. Math. Soc. (1984) 327 MR780587
40	C Livingston, Seifert forms and concordance, Geom. Topol. 6 (2002) 403 MR1928840
41	W Lück, T Schick, Approximating $L^2$–signatures by their compact analogues, Forum Math. 17 (2005) 31 MR2110537
42	W Lück, T Schick, Various $L^2$–signatures and a topological $L^2$–signature theorem, from: "High-dimensional manifold topology", World Sci. Publ., River Edge, NJ (2003) 362 MR2048728
43	T Matumoto, On the signature invariants of a non-singular complex sesquilinear form, J. Math. Soc. Japan 29 (1977) 67 MR0437456
44	K Murasugi, On a certain numerical invariant of link types, Trans. Amer. Math. Soc. 117 (1965) 387 MR0171275
45	A A Ranicki, On the Hauptvermutung, from: "The Hauptvermutung book", $K$–Monogr. Math. 1, Kluwer Acad. Publ. (1996) 3 MR1434101
46	A Ranicki, High-dimensional knot theory, Springer Monographs in Mathematics, Springer (1998) MR1713074
47	D Ruberman, Doubly slice knots and the Casson–Gordon invariants, Trans. Amer. Math. Soc. 279 (1983) 569 MR709569
48	D W Sumners, Invertible knot cobordisms, Comment. Math. Helv. 46 (1971) 240 MR0290351
49	H Terasaka, On null-equivalent knots, Osaka Math. J. 11 (1959) 95 MR0117736
50	H F Trotter, On $S$–equivalence of Seifert matrices, Invent. Math. 20 (1973) 173 MR0645546