Algebraic & Geometric Topology Volume 17, issue 1 (2017)

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Double $L$–groups and doubly slice knots

Patrick Orson

Algebraic & Geometric Topology 17 (2017) 273–329

DOI: 10.2140/agt.2017.17.273

Bibliography

1	E Bayer-Fluckiger, N W Stoltzfus, Stably hyperbolic 𝜖–Hermitian forms and doubly sliced knots, J. Reine Angew. Math. 366 (1986) 129 MR833015
2	T D Cochran, K E Orr, P Teichner, Knot concordance, Whitney towers and L²–signatures, Ann. of Math. 157 (2003) 433 MR1973052
3	D Crowley, W Lück, T Macko, Surgery theory, unpublished textbook in progress (2015)
4	R H Fox, A quick trip through knot theory, from: "Topology of 3–manifolds and related topics", Prentice Hall (1962) 120 MR0140099
5	C Kearton, Cobordism of knots and Blanchfield duality, J. London Math. Soc. 10 (1975) 406 MR0385873
6	C Kearton, Simple knots which are doubly-null-cobordant, Proc. Amer. Math. Soc. 52 (1975) 471 MR0380817
7	M A Kervaire, Les nœuds de dimensions supérieures, Bull. Soc. Math. France 93 (1965) 225 MR0189052
8	T Kim, New obstructions to doubly slicing knots, Topology 45 (2006) 543 MR2218756
9	C F Letsche, An obstruction to slicing knots using the eta invariant, Math. Proc. Cambridge Philos. Soc. 128 (2000) 301 MR1735303
10	J Levine, Knot cobordism groups in codimension two, Comment. Math. Helv. 44 (1969) 229 MR0246314
11	J Levine, Knot modules, I, Trans. Amer. Math. Soc. 229 (1977) 1 MR0461518
12	J Levine, Doubly sliced knots and doubled disk knots, Michigan Math. J. 30 (1983) 249 MR718271
13	J P Levine, Metabolic and hyperbolic forms from knot theory, J. Pure Appl. Algebra 58 (1989) 251 MR1004605
14	C Livingston, J Meier, Doubly slice knots with low crossing number, New York J. Math. 21 (2015) 1007 MR3425633
15	J Meier, Distinguishing topologically and smoothly doubly slice knots, J. Topol. 8 (2015) 315 MR3356764
16	P Orson, Double L–theory, PhD thesis, University of Edinburgh (2015)
17	P Orson, Double Witt groups, preprint (2015) arXiv:1508.00383
18	M Powell, A second order algebraic knot concordance group, PhD thesis, University of Edinburgh (2011)
19	A Ranicki, The algebraic theory of surgery, I : Foundations, Proc. London Math. Soc. 40 (1980) 87 MR560997
20	A Ranicki, The algebraic theory of surgery, II : Applications to topology, Proc. London Math. Soc. 40 (1980) 193 MR566491
21	A Ranicki, Exact sequences in the algebraic theory of surgery, 26, Princeton University Press (1981) MR620795
22	A Ranicki, High-dimensional knot theory, Springer (1998) MR1713074
23	A Ranicki, Blanchfield and Seifert algebra in high-dimensional knot theory, Mosc. Math. J. 3 (2003) 1333 MR2058802
24	D Ruberman, Doubly slice knots and the Casson–Gordon invariants, Trans. Amer. Math. Soc. 279 (1983) 569 MR709569
25	D Ruberman, The Casson–Gordon invariants in high-dimensional knot theory, Trans. Amer. Math. Soc. 306 (1988) 579 MR933307
26	N W Stoltzfus, Unraveling the integral knot concordance group, 192 (1977) MR0467764
27	N W Stoltzfus, Algebraic computations of the integral concordance and double null concordance group of knots, from: "Knot theory" (editor J C Hausmann), Lecture Notes in Math. 685, Springer (1978) 274 MR521738
28	D W Sumners, Invertible knot cobordisms, Comment. Math. Helv. 46 (1971) 240 MR0290351
29	C T C Wall, Surgery on compact manifolds, 1, Academic Press (1970) MR0431216
30	C A Weibel, An introduction to homological algebra, 38, Cambridge University Press (1994) MR1269324
31	E C Zeeman, Unknotting combinatorial balls, Ann. of Math. 78 (1963) 501 MR0160218